I trust you on that, and there has been rumours about how the two wouldn't get along because of the system, but you have to understand, Payton wasn't all that important at that point. If all things fail, there's still Fisher. He may have been a corpse at that point, but he knew the system and accepted his role.
The Lakers were dysfunctional, and everybody knew it for the last 2 years or so, but they still won championships. And as you mentioned, they STILL made the finals by beating a historically good Spurs defense (and equally bad offense) in the very tough west, so they must be good at something.
And as I said, nobody expected the Pistons to win that series (except Pistons fan and you). Everybody wanted the Pistons to win, but no one expected them to.