I think he can be trusted. After all, the Dragonborn defeated him in combat, and in the dragon culture (?), being powerful is the same as being right. Then again, if the Dragonborn shows any weakness, either proving they're weaker than Odahviing, or after another proves their strength, then there might be an issue.

Cloth-equipped iron dagger-wielding commoners can easily take down a dragon
) your PC can trust him in that extent. As for the rest of Nirn, hmm unsure tbh, unless the LDB can convince him.