I think that was the point of her saying Jon Snow betrayed her. Fact is he set in motion a chain of events by telling his family about his birthright that would ultimately put him in head to head conflict with Dany. She knew that and that's why she tried to swear him to secrecy.

Now the situation is you have an angry populace and a war hero walking around who is rumored to be the rightful heir to the throne. He is the biggest threat to her rule and she has to try and take him down.


**********
"Everyone has a plan until you punch them in the face. Then they don't have a plan anymore." (c) Mike Tyson

"what's a leader if he isn't reluctant"