The story was never officially confirmed. On the other hand, I doubt that anybody who knows a bit about how such things are handled in Japan would ever expect it to be, even if it is true.
I, for one, happen to absolutely believe it, and I will give you my reasons why. Combined, they do not even leave the shadow of a doubt, as far as I am concerned:
1. Akishino´s reputation
According to
an article by Edward Klein who once worked as foreign correspondent for United Press International in Asia, Akishino´s nickname as young man was „Fast Hands“ because of his reputation as heavy drinker and womanizer in Tokyo´s night clubs and discos. Klein says that Akishino´s intimate relationship with his girlfriend Kiko became a matter of serious concern to the court, especially as Kiko´s father was intervening, and that this was the real reason why Akishino was allowed to marry before his elder brother (which was unprecedented and completely against tradition).
I´d like to add that, if this point were the only “circumstantial evidence” in this case, I would certainly completely dismiss it. People can change, and they sometimes even do. But within the context of the following reasons, I do find it significant to note that Akishino has already earlier given proof that he is capable of acting in a way that could easily be called careless and irresponsible.
2. The (Un)importance of being Clinton
I am convinced that we would never have heard of this affair – if true or not – if then-president Clinton had not been involved in it, in a certain way: In April 1996,
the media reported that Prince Akishino would miss a state dinner with Clinton, allegedly because of a “previous commitment” to travel to Thailand for a festival dedicated to the rare giant catfish, at the time in season in the Mekong River. But later the gossipy weekly magazine
Shukan Shincho claimed that the prince was on "intimate" terms with a Thai woman, and that this had been the real reason for the trip to Thailand. The editor of Shukan Shincho, Hiroshi Matsuda, justified his decision to print the article by saying the prince's absence from the Clinton banquet could have offended Japan's most important ally and therefore needed to be explained.
Now let´s take a closer look at these facts: First, one wonders what could have been so urgent about catfish that Akishino felt obliged to miss a state dinner for it. It is to be supposed there is a catfish season in Thailand every year whereas the US president doesn´t visit Japan that often. (And even if he did, that would hopefully not always happen during the catfish season...
) It is true that Akishino is known as a “catfish specialist” and that, at the time of the banquet, he might have been working towards a PhD degree that he was to receive in October of the same year. But: the degree was
in ornithology. The doctoral dissertation was titled, "Molecular Phylogeny of Jungle Fowls, genus Gallus and Monophyletic Origin of Domestic Fowls." Considering this, it becomes even more of a riddle why Akishino felt in spring 1996 such an urgent need to attend a giant catfish festival. Obviously, it would have been much more plausible if he had missed the Clinton dinner in order to travel to some sort of a “Jungle Fowl festival“ that could have helped him with his thesis...
All things considered, I, for one, think that whatever the real reason for Akishino´s absence was, it cannot have been the one that was officially given. So that leaves us with the question: what then
was the real reason? It must have been a strong one because, even if Akishino might personally not have been very keen on meeting Clinton, he must have been aware that his absence would be publicly noticed and might get him into serious trouble (which in fact has happened). Besides, the real reason must have been one that could not be officially admitted. Of course, I could come up with several alternative possibilities to the explanation offered by Shukan Shincho (that Akishino was impatient to see his mistress). For example, Akishino might have been suffering from some strange illness that is considered shameful in Japan and might have been going to see a famous spiritual healer in Thailand about it, and for some reason it was impossible for him to postpone this visit... But just like this fanciful example, everything else I could think of as a plausible reason for Akishino to visit Thailand at exactly that time, seems very very far-fetched compared to the very easy and common explanation of him meeting a woman there...
3. The press conference
Another point that is very remarkable regarding this story is that Akishino took the highly unusual step of explicitly denying the allegations at a news conference. (The usual imperial way of handling disagreeable reports or rumours would be to completely ignore them, to “kill them with silence”.) Besides, I find it very interesting how Akishino worded his protest on the occasion. He said, "Smoke has risen where there is no fire." To me, this comment seems to be like taken directly out of a psychology textbook. The proverb says: where is smoke there is
always fire. It seems to me that this expression of the prince was a Freudian slip. Of course, it is clear that this is no more than a personal feeling of mine and that others may find this interpretation absolutely silly. But there is another reason still why I believe the story, and that is, in fact, the most important:
4. The stubbornness of the editor
After the prince´s press conference, the editor of Shukan Shincho, Hiroshi Matsuda, said, "I have absolutely no intention of issuing a correction. . . . I still believe the story is true."
Now this is highly remarkable because the Japanese media (unlike their European counterparts) generally treat the imperial family with extreme deference. There are several examples of Japanese media keeping quiet about facts that they were perfectly acquainted with and already knew to be 100% true, out of respect for the IHA and the imperial family. (Famous instances of the Western press breaking Japanese imperial news before the Japanese media dared to even touch the issue would be Masako´s engagement to the crown prince and later, the fact that she had fallen seriously ill.)
As I said, the imperial household usually tends to ignore disagreeable stories, but as in this case Akishino had already taken the trouble to explicitly deny the allegations, the editor could not even be sure that the IHA would not take the matter to court – which could easily have become a really mortifying experience for Matsuda -
if he was not 100% sure that he would be able to prove his assertions. For me, it is absolutely clear: If the editor, in such a situation, explicitly insisted on the story to be true, even against imperial protests - which he did -, I bet he had a
really trustworthy source for it.
Besides, I would like to note that many instances worked together in this case to make the story publicly known: Clinton could have chosen another time for his visit/the catfish festival could have taken place at another time/whoever told the editor about the affair might have kept his (or her) mouth shut/the editor might not have the guts to publish the story. If but one of these circumstances had been lacking, nobody would have been even speculating about an imperial affair in Thailand.
In my opinion, this clearly demonstrates that there might be quite a lot of things going on at the imperial court that we never ever hear anything about. To be blunt: Akishino could have a mistress in every country he occasionally uses to visit without his wife, for scientific research, in Thailand, in Vietnam, in Indonesia, plus the Japanese court journalists could be perfectly aware of this. But the chances would be still
very scarce for us to ever hear one single word about it.
I know that this forums does not accept "I heard on TV... or I read somewhere..." as a sufficient proof, but I am unsuccessful in my attempts to provide a link. 
I just had not heard this myself and am not suprised by it. Prince Tomohito's remarks caused such a stir at the time because the debate about the possibility of Aiko ascending was raging. The subtlety of public remarks by the Imperial family are such that they would seem to be saying one thing and really implying something else. So while the IHA would like Akishino's remarks to be seen as helpful, they could be perceived as suggesting something altogether different. For my part, I believe that Akishino is trying very hard to reform his image as the Imperial bad boy and solidify his position as his parent's protector and father of the long awaited male heir. In short, better Emperor material than Naruhito.
Otherwise she´d be a saint. 
