Have you seen The Dark Knight movie? I realize it is a work of fiction, but there is one instance in the movie that looks like a pretty clear-cut example. Remember the Chinese businessman dude (I think his name was Lao)? He was working with the mob in Gotham City. He had assured the mob that he would keep their money safe... and that what would prevent law enforcement from coming after him would be returning to Hong Kong. Since China is far, far outside the jurisdiction of the GCPD, Lao would have gotten away with his criminal activity... (while at the same time protecting the mob's assets, which would keep them safe in their illegal operations).
Batman, of course... is not a part of the GCPD ("Orders are to arrest the vigilante known as Batman on sight"). He doesn't have a jurisdiction. He doesn't have anyone to answer to. Yes... He essentially went to China and KIDNAPPED Lao... But he brought him back to the GCPD, so that he could face justice. In the process, it helped taking down the mob much easier.
Superheroes would be able to work where policemen couldn't. And if the superhero really is a superhero, this would be a good thing.
In the movie, that could reasonably be painted as a good move.
If Batman pulled a stunt like that in the real world, it would be a disaster. Diplomatic incident. China wouldn't exactly appreciate an American agent - even an unofficial one - kidnapping one of their citizens so that he can be imprisoned in America. And if the police start relying on superheroes to break the law, then that means superheroes have become a way for the police to bypass the very laws that exist to prevent them from abusing the system. At which point, society becomes a de facto police State.
You say it would be a good thing if the superhero really is a superhero. Well, duh. If every policeman was Jim Gordon, there would be no need to worry about police corruption. If every politician was honest, we wouldn't need laws against bribery. If every lawyer was Atticus Finch...But, they aren't. And again, the law cannot function on a case-by-case basis; it must account for the bad elements, and leave a safety margin.
If your system depends on all the superheroes (or even a majority of them!) being Clarck Kent or Peter Parker...it's going to fall apart real quick once real people get involved. Just because most of the superheroes in Marvel and DC are untouchable, that doesn't mean we should expect the same in a realistic world.