Definitely not. Just because one has super powers doesn't mean they're suddenly above the law. The Justice League knew that when they established the "No killing" rule. They may have abnormal strengths and abilities to help protect the world and its people, but they're no better than the enemy if they're out to kill.
However, there are certain laws superheroes and lesser powered heroes, Batman for example, are going to have to break and we as society are going to have to forgive them for. That's just part of the job. As a hero, you have to make tough decisions; decisions not everyone is going to like and decisions that aren't always going to play by the rules. If they're out defending lives and doing a whole lot better than local police, then who are we to stop them?
Overall, I see it as a bit of a give and take in this situation. So long as they aren't committing outrageous criminal acts such as taking the lives of others, then I feel like they can be forgiven for other smaller offenses. Otherwise, they're just as equal as humans under the law, superpowers or not.