HOW would she be offered to be given teh style of Princess Diana?? there is no way that that could happen. Princess Diana would only be if she was the daughter of a king or prince...
It's a technicality, but "Princess Diana" is not a style, it's a title.
The Queen can theoretically bestow royal titles on whoever she wants to, so if she had wanted to make Diana a Princess in her own right she could have - likewise with Camilla, Catherine, Sophie, Sarah, and similarly with Tim, Mark, and Anthony - as she did with the DoE. She could ask decide to allow a woman who is a British Princess by marriage to use her own name in her title, instead of her husband's - if she wanted to, she could go to Princess Michael of Kent and say "from now on I think you should be called Princess Marie Christine of Kent".
But, doing both kind of goes against British tradition and custom, and so it's kind of unlikely.
that's hardly teh same, he was made a prince as he was the queen's husband. Diana was hardly goig to be given the privilege of being "Princess Firstname.." when she was leaving the RF.. People kept saying this a few years ago when Kate married William, that she was going to be given the title of "Princess Catherine" rather than "Princess William or HRH the Duchess of X".. which was not going to happen.. The only time the Q has done this was to give Princess Alice duchess of Gloucester the right to call herself Princess Alice, and that was when she was the wife of a prince and had done a lifetime of royal service. I dont beleive there was ever any "offer" that Di would be "Princess Diana".
In a way, Princess Alice wasn't the only wife of a British Prince to use her own name, and the circumstances were very atypical.
King George V had 4 sons to survive into adulthood, Edward, Albert, Henry, and George, who married Wallis, Elizabeth, Alice, and Marina. Edward, of course abdicated in order to marry and his wife was denied the right to use her husband's Royal styles, remaining "simply" a Duchess. Albert became King, so Elizabeth became Queen, and Marina was a Princess of Greece and Denmark in her own right.
Legally, as she became a British subject after her marriage, Marina wasn't supposed to use her foreign titles, but after her husband's death and her son's later marriage she decided she didn't want to be titled as The Dowager Duchess of Kent and asked to be able to use her own name. The Queen allowed it, and so she became known as Princess Marina, Duchess of Kent.
Going forward to 1974, there were 3 surviving daughters-in-law of George V - Wallis, Elizabeth, and Alice (Marina having died in 1968). Wallis was still denied the use of Royal titles, Elizabeth was Queen Elizabeth, the Queen Mother, and Alice was the new Dowager Duchess of Gloucester, her husband having died that year and her son already being married. So, as the only daughter-in-law who was both recognized as a Royal and not having a title of her own, it was kind of logical to have her use Princess Alice, Duchess of Gloucester (similar to Marina), instead of The Dowager Duchess of Gloucester (more comparable to Wallis).