No it doesn't.
Whoever told you that was either misinformed, or were promoting their own agenda.
Yes, but that purchaser has distribution rights. So they'll basically sell it a few hundred times per release, if even.
Intel open source their graphics cards drivers on Linux and don't have a problem with doing that. Valve have recently been spending money working with Intel on those drivers precisely to allow better performance of games on Linux.
That's because Intel's graphics are essentially a service provided to customers. They in no way thrive or depend, at all, on their GPUs. ATI and Nvidia don't open source their drivers because they wouldn't have a unified platform for developers to release on. Any functionality added by the community wouldn't be supported by devs because it would severely limit their target demographic.
Microsoft themselves have contributed large amounts of code to open source works.
The Steamworks API is closed source but is not being released with any cost for developers to use, and is frequently updated.
Is this even relevant?
There is literally no reason why a company 'must' charge
Except for the fact that, to compete with DirectX, a massive team would need to be assembled to work on it full time. That wouldn't just happen by community support. A company would NEED to take charge of developing that API, and a company obviously COULDN'T survive if it didn't charge for its product.
DirectX is starting to show that it's going to forcibly take lead in the API war with DX11. It's getting to a point where the organization of Khronos won't be able to keep up with the development of DirectX.
That's mostly speculation, but apart from there being a number of Open Source licences that are not GPL (and something like Apache is very popular) the drivers for both ATI and Nvidia are both used by Linux owners and closed source.
People use them, because they have no real alternative not to.
It would be better off for everyone if ATI and Nvidia open sourced their drivers, because it would mean they were updated more often.
It would be better off for Linux users to have a more functional machine, but it would fudge the line for what is and isn't supported by each user. You'll end up with a bunch of forks from different versions, and the userbase will be segmented and progress slow, just like the Android platform now.
Regardless, because of the structure of GNU/Linux and the nature of a company to keep its source closed, it just won't be happening there. GNU/Linux just isn't a viable platform for something of such complexity and time investment.
I get that all of the GNU/Linux users want to live in some happy-go-lucky world where source code is free to roam the plains and any man can do as he pleases, but that's directly contradictory to the corporate structure of the world today.