I'll pass on the suggestion that Parcells is JC and Belichick is one of his disciples.
No one said that BB was "uninfluenced" by Parcells, just that his own formation as a coach began way before his time with Parcells. And, describing Belichick's relationship to Walsh as "reading books about" him is just plain wrong.
Finally, statistics can be abused in forming a view in any sport, but in this case the data on Parcells record with and without Belichick are simply overwhelming. He never won without him.
Here's a quote from the late David Halberstam during an interview with WEEI in November 2005 that addresses the relationship between Parcells and Belichick.
I've left in the entire quote and haven't edited it to "make my point." My point is that Parcells the motivator didn't win a thing without Belichick, and Belichick went on to win plenty on his own.
"...the original person who brought them [Parcells and Belichick] together was Ray Perkins, the very tough guy who was to be Bear Bryant's successor at Alabama. He brought them in, and they couldn't be more different. Parcells is the living embodiment, to the degree there is one, of the Vince Lombardi prototype of coach – emotional, making players go in hitting the emotion, getting guys to play harder, and making them feel they're wimps if they can't do it. And then Bill Belichick, who is really, although on defense, a kind of lineal descendant of Bill Walsh – cerebral, doesn't play with the emotions of his players, thinks that everything can be broken down and analyzed. But they came together and it really worked. Parcells knew how to run a team, how to get the emotions, and Belichick was the creator of those great defenses with great players. They stayed together too long. It got harder and harder, I think, the more Belichick got to parity. The more people began to give him credit, I think, the more it grated on Parcells. And they probably should have gotten divorced about two years before they did."