It's important to realize that "Photograph 51" wasn't "Franklin's" -- it was taken by Raymond Gosling, a grad student mentored by Franklin and Maurice Wilkins. What happened was that Wilkins chose to share the data with Watson and Crick. Yes, he maybe should have consulted with Franklin first (and certainly with Gosling, whose opinion nobody seems to care about).

In any case, while Franklin certainly didn't get along with Watson, she was close friends with Crick and his wife Odile up to her death and in fact lived with the Cricks when she was undergoing treatment for her cancer [2]. This would be hard to square with the idea that she thought Crick had "stolen" "her" data,

[1] https://en.wikipedia.org/wiki/Raymond_Gosling [2] https://en.wikipedia.org/wiki/What_Mad_Pursuit