Check this out:
http://developer.nvidia.com/object/physx_downloads.html
Literally anyone can download the SDK for free. So why hasn't it "taken the world by storm" as you said? It's proprietary. NVIDIA claims that PhysX, along with CUDA, is open to any hardware should one want to support it. The most likely reason holding AMD back from doing this is the unbalanced performance prospects of such an implementation. They probably don't feel like they need to anyway, since more open standards like Bullet physics will eventually arise to make use of OpenCL.
Of course if AMD was so confident in OpenCL, they might be more enthusiastic to get a working driver out for it, but as it is, even NVIDIA has beat them to the punch there. AMD makes great hardware but they really suck in the software/developer support side compared to the competition.
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