The NSA can not only file for patents, they can do so secretly.

From wikipedia:

The NSA has the ability to file for a patent from the U.S. Patent and Trademark Office under gag order. Unlike normal patents, these are not revealed to the public and do not expire. However, if the Patent Office receives an application for an identical patent from a third party, they will reveal the NSA's patent and officially grant it to the NSA for the full term on that date.

As has been pointed out above, Microsoft does, in fact, make an OS that must be installed on Microsoft hardware, namely their XBox OS. Sony and Nintendo do the same thing, so do most (if not all) cell phone and smartphone manufacturers.

Apple created their OS, can can license it however they choose. What give you, or any consumer, the right to unilaterally disregard the licensing agreement for OSX? If Apple is creating a good product, but are selling it with a over-restrictive license, that looses them sales, then that is certainly bad business practice, but there is nothing illegal, or immoral about it, and nothing gives you the right to decide that you don't like how Apple is selling their product, and do whatever you please with their work.

And as for Psystar not modifying the OS at all, I was under the impression that, at least initially, they did need to modify the OS, and that they still take and modify the various updates and patches to work on non-Apple hardware. In fact, i'm pretty sure that one of the central thrusts of Apple's case is the modified security and other patches that Psystar provides.