black and white/ spidey punisher comic book morality
While the Punisher may have a rather black & white view of morality (matches the outfit nicely), when he interacts with Spider-Man he represents a very grey area. That's pretty much the point of him as a character in Spider-Man's world: someone who fights evil but crosses a line that, in Spider-Man's eyes, makes him almost as bad as the people he fights, forcing Peter to question whether he should be working with him or against him.
Even without the Punisher around, Spider-Man morality has rarely—if ever—been a black & white affair. Peter is constantly struggling to find the right way to do things, balancing the cost of his overdeveloped sense of responsibility against the fact that it means spending most of his life living a lie. He lies outright to the faces of people who love him and who have put trust in him. Over the years, the majority of the money that Peter Parker has ever made depends on taking pictures of himself and pretending he's not the subject of his own photographs, which seems rather fraudulent.
On most black & white approaches to morality, he'd have to be judged as a rather immoral person, despite all of his good deeds. Either that, or we have to assume that it's a black & white system in which lying to people isn't ever immoral. Once you start saying that it's moral in some situations, we're starting to add grey areas.