OK, I tested my old controller on my XBox 360 with multiple games: Geometry Wars 1 and 2, Aegis Wing, Marble Blast Ultra, and they all handle the dead zone properly. None of them show motion when the controller isn't being used. I tapped the controller to attempt to force this to happen at least 100 times per game.
The same controller on my PC (I assume this doesn't matter, since the raw hardware values are computed inside the controller, but perhaps the fact that I'm using a PC does make a difference?), with the XNA Framework, will report, on occasion, after 40 or 50 flicks of the controller, values near 0.250 when there's no motion. Such values break the XNA dead zone handler (i.e. it reports as motion) when using GamePadDeadZone.Circular.
Please note that this occurs with GamePadDeadZone.Circular only, not with GamePadDeadZone.IndependentAxes. If these XBox 360 games use something like GamePadDeadZone.IndependentAxes code (they shouldn't, but perhaps they are), then their code could be using identical to the XNA Framework. However, if they are using GamePadDeadZone.Circular style code, then they handle the dead zone for my older controller better than the XNA Framework.
In any case, programming your own dead zone handling is easy as pie, and I need only loosing the tolerance slightly to make it work for my controller, as well.