Yes, she had a paper, hastily thrown together because Watson and Crick were going to publish her data without her consent, and even to the men of 1952, what they had done to her was seen as pretty scuzzy, so they tried to give her an opportunity to at least claim a little credit. But this is a sign that even the the people around them saw that Franklin had been done wrong by Watson and Crick and Wilkins.
As far as "she shared it in a departmental seminar once, therefore her boss can just give it to others to beat her in the analysis phase without her consent" and "I don't think she would have gotten it right," neither of those are actually arguments. One of them is not how science is supposed to be done, the other is an un-provable assertion that a woman wasn't smart enough to figure something out, which makes me a little suspicious.
How exactly did you get to "a woman wasn't smart enough to figure something out, which makes me a little suspicious."? It sounds like you're saying I think she wasn't smart? I am merely reporting the facts as they have been reported, based on a number of different books/articles.
It was an intrinsically hard problem that Crick was especially prepared to solve. I doubt the vast majority of scientists, regardless of their sex, would have been able to solve the problem with the data they had.
Generally once you share data publicly, there is a blanket rule that people can use that data. Many people claim W&C stole the data (through Wilkins) but that does not seem to be true.