2. Walks into Solitude unannounced and challenges the king. There is no mention of the High King accepting the challenge or putting up a good fight back.
Ulfric is a coward, yes, but Torygg did accept the challenge. Torygg knew he would lose the fight, but bravely accepted the challenge because despite what Ulfric would say, he was no milk-drinker. We know this because when you meet Torygg in Sovngarde, he flat out says it. Side note, if you meet Ulfric in Sovngarde, he lets bygones be bygones, and even admits that his war was a huge mistake.
Ulfric likes to boast about how he killed Torygg "because he could" and "because he wanted to show people how weak one is when they drink the empire's milk", but in reality, he's full of crap. We know nothing about Torygg's martial skills, we only know Ulfric won because he used the Thu'um. If you challenge someone to a duel, you are in general, agreeing to play by a certain set of fair standards. When one party has an insurmountable advantage like the Voice at their disposal, and the use it? It stops being a duel, it turns into murder.
So the claims from each side that it was a duel, and also that it was murder? Both are true. Torygg accepted the challenge, Ulfric used a ridiculously overpowered unfair advantage, and then had the nuts to boast about it like he was something special. It was dishonorable.