nVidia will let you run PhyX, you just need to run CUDA first, and provide nV with all your architecture details, and most people don't want to do that.
It's not an Open Standard, and it's not like nV doesn't have its strings in their 'offers', just like it was free, then Free, then REALLY FREE.
Also Gamer, the PhysX being used on Xbox and Wii (which uses an ATi Hollywood GPU) are NOT GPU-accelerated, they are plain PhysX engine, just like the non-GPU-accel version of Havok.
To the OP, DX11 and PhysX are mutually exclusive in and of themselves, but both the compute shaders of DX11 and the options of OpenCL (and it's support by AMD, intel for Havoc, and S3 in principal) means PhysX's 'need' is greatly diminished, and people would prefer an unbiased standard, something akin to the DirectPhysics everyone wanted long ago during the intial GPU/PPU-physics discussions.
As to what both DX11 and PhysX means to future titles, no one knows yet except for those on pre-release software and hardware. Like everyone else, you'll just have to wait see what.... wicked this way comes.