Actually, you do know how I run my games.

That sounds pretty spot on.
To give an example of the two different styles, as I see them, it's like Spider-man and Superman. I like Spider-man. He's a hero. But he has conflicts. Angst. Personal problems. My mentor likes Superman. Definitely heroic. But not in the same style. My favorite author is Tim Powers, a writer who knows how to do terrible things to his characters. In the end, they do heroic things. But lots of personal anxiety going on there, times when they want to quit, times when their past catches up with them (or future, as the case may be). Those are the kinds of games I run.
I'm not convinced I don't give players a chance to be heroic. But it may not be the style D&D is intended to represent.