She shouldn’t in my book. The Prince of Wales is the heir, the Princess is the consort of a sovereign. In my book, he should nod to her and she should gracefully accept his respect for her station. Then again, royalty who has married into royal families tend to make these errors from time to time. I would hand it down to a bit of nerves and a wish to avoid mistakes, therein leading to the mistake. As far as
mistakes go however, this is certainly the smallest one to make. The only reason it’s a little more fun than some others, is the visibility of it
There is another side of the argument that some have made, and that is that titles reflect different ranks of royalty. For example, as heads of state, most presidents and kings do not bow to the only emperor left, the Japanese one, but some, including Obama, have chosen to bow, and that is technically not wrong. The rank of Emperor is the highest one to be had in our world of titles, whereas kings and presidents would be equalled at tier 2 of a ‘ranking ladder’. Royal Highnesses outrank Serene Highnesses, who would equal Grand-Ducal Highnesses, who all outrank Highnesses etc etc.
However, in the world today, it would appear to me that most would equalize one head of state with another, regardless of title, with the possible exceptions of an Imperial Majesty and His Holiness the Pope, who for historical and religious reasons are still held in the highest tier of esteem and reverence. After that, one sovereign does not need to bow to another, but can choose to, as, again, it is simply a mark of respect and not the claimed act of subservience by those who have little historical or cultural appreciation.
An heir to a throne would genuflect/bow to a sovereign, and a member of a royal family would do the same to any other member who outranks them. Everyone else, from ministers to citizens, who choose to follow the custom, would genuflect/bow to all of the above in an encounter and would never be wrong for doing so.