No that’s where you are just plain wrong. She is a Senator who is captured in an act of espionage and is a leader in military resistance to the Empire. She can resist Vader’s powers and standard Imperial interrogation techniques and is really handy with a gun. So not just some posh Princess. She isn’t even that posh when she is talking to Han and Luke.
Interrogation was basically purely on mental level and it doesn’t mean too much in this context. She could simply be good at resisting truth serum. It is not like she was being beaten up. Same goes for her skill with a gun. It doesn’t mean a thing as she could as well gain that skill on luxury “safari” hunts.
The thing is that she is plain annoying after she is being rescued. With that kind of annoying attitude and lack of charisma, it is really implausible that she would be able to lead anyone. But anyway, she didn’t need to as she was a spy in elite circles.