Andrew Jackson was a barbarian then.
And you're saying he didn't do many barbaric things? Heck, he was even heavily criticized in his day for his duel. That's kind of the tip of the iceberg with him, honestly.
Nope. Either attack the arguments or give it up. Any man has a choice. It doesn't matter if he'd lose face or not, it's still his choice. He knew nordic law just as Ulfric did. If he had said no it would've went to the moot. If he wanted a way without bloodshed that was it. Either make a case why you're fit to lead or step down. Torygg accepted either because he was young and foolish, or he didn't think he had a compelling claim to the throne.
Right, so ignore the entire culture the man grew up in and was living in. Context doesn't matter making political, social, or similar decisions. It's irrelevent. Hilarious point of view you got there.
Your character doesn't have Stormcloack clothings on him when you start the game, just like another one who claimed his innocence, that other prisoner from Rorikstead.
Not that they'd necessarily expect everyone in a ragtag rebellion to be wearing uniforms. Heck, many times in history militaries haven't been able to equip all of their own men with uniforms. So that doesn't really mean much.
I'm not saying they were right in choosing to execute you or the horse thief, and certainly ideally even Ulfric would have had a trial. I'm just saying it is far from clear that you aren't a Stormcloak.