Batman often works outside the system, and enacts his end pursuit in a manner that those more often described as lawful would object to. Yes, it is dependent on the writer, but the last time he was truly lawful was when he was played by Adam West. Sinestro alternatively resorts to accomplishing his end goal of galactic peace via tactics that could be simplified as terrorism. He wishes to implement a lawful society that he would lead and simply resorts to less than savory tactics in order to accomplish and preserve his lawful rule. Black Adam and him get along because of their similarity. They aren't cartoon baddies. They respect the law, and wish to defend it. Their problem is that the methods they often resort to in order to do so often fall out of the realm of good. When the universe has been at risk however, Sinestro has stood beside traditionally good characters to defend it, as has Adam in less severe circumstances.
Also, the ring didn't take, because Bruce willed for it not to, not because it was a mistake that he was chosen. At a later point, Sinestro complimented him by telling him what an exceptional member of the Sinestro Corps he could have been has he chosen to be.>>86620783>Criminals are a fearful and cowardly lot>I'm going to bring about peace in the universe by scaring everyone in it into behaving well>>86620967
Sinestro acted tyranically on his planet, but accomplished peace by ruling with an iron fist
Batman often fights public servants and other superheroes as often as he fights his own rogues gallery because of his unilateral decision that he is justified in doing so.