Anyone who can look at the 2001, 2004, 2007, and 2011 offenses and conclude that the guy who excelled in all of them is a 'system' QB is just dumb, plain and simple. Mostly because those 5 offenses are radically different, featuring radically different personnel, philosophies, positions of emphasis, areas that they like to attack, etc. Brady has excelled in a ball control offense, a dink and dunk offense, a shotgun spread offense that bombs downfield, a 2 TE base offense that attacks the seams, etc. You could probably argue that half the reason why the Pats have been able to evolve their personnel and base strategy so much is precisely because Brady isn't tied to one specific style. He's good in pretty much any passing offense, provided that you aren't doing something super dumb like asking him to roll out all the time or run the read option or some other similar fad.
This is why you'll never see Brady being a slightly above average QB for a whole year like Rodgers has been, solely because his favorite receiver got hurt and the Packers are unwilling/unable to adapt. That's the kind of inflexibility that you'd expect to see in a 'system' team. The Pats, OTOH, are the opposite. And in Rodgers' case, he can play his entire career in the same exact offense, an offense in which his backup can come in and throw for 500 yards and 6 TDs in that offense, but nobody has ever claimed he's a system QB. Which is good, because he's not, but it's even more ridiculous to claim that Brady is. And Manning can be so married to his ideal offense that Gary Kubiak had to basically throw out his playbook and use Peyton's to get anything at all out of the guy, but somehow nobody suggests he's a system QB either. Only Brady, despite the fact that Brady has proven far more scheme-versatile than either of them.