[EVERYTHING] Arya isn't a complete dolt.

Politics obviously wouldn't be her strong suit but it's not like she doesn't have any skills that would be useful in her new setting, learning to lie and detect lies was a huge part of her story while she was at the House of Black and White. Furthermore, she knew Sansa was a prisoner at King's Landing, she had to hide her identity and pretend to be a boy for the very same reason. You don't need years of political experience to come the conclusion that a message sent by a political prisoner may have been written under duress.

I don't understand why the letter she found would have upset her to begin with, even if she did believe Sansa wrote it willingly. It was an attempt to prevent war and spare their father's life. Robb would have marched on King's Landing either way, Joffrey would have executed Ned either way. Blaming Sansa for any of it because she urged for peace literally makes no sense. It was an odd choice on Littlefinger's behalf even for a red herring.