They are not in the business of supporting operating systems other than Mac OS X. Why should Apple techs provide support for an operating system they do not make?
Nobody is asking them to support Linux. If I call their support and say I have trouble sending emails, of course they won't troubleshoot the issue if I'm using Ubuntu, because it has nothing to do with their products. But if I say that my enter key doesn't work or that my fan is very loud, the OS shouldn't matter.
You expect them to do a fresh install of OS X themselves just to test it out?
I'm quite sure that even with users who have OS X installed, they don't use the installation on the machine to install their diagnostic software and do the testing. What if the machine doesn't have enough space? What if it's password-protected? What if it has some kind of software that's incompatible with their diagnostic tools?
Most bigger tech-support departments are well prepared for these situations and simply swap your hard drive or boot from an external harddrive/CD with pre-prepared software to do their testing the proper way. They can do that regardless of the OS you're currently using.
The combination is what is supported, not the individual parts. They have the documented right to refuse you service if you're not running OS X.
To use an APPLE analogy, because cars have NOTHING to do with this and Apple is the ONLY thing that matters here, it's like when the Bluetooth chip in your iPhone is defective, but they deny you service because you're jailbroken.
They couldn't care less about the hardware on its own.
No, that's different. Yes, they are selling the combination of hardware and software, but they allow you to change some things and disallow you to change others. Adding RAM or installing a different OS on your laptop is allowed, as is installing apps and getting new earbuds for your iPhone.
Jailbreaking the iPhone means touching it the way they don't want it to be touched, you void your warranty and they won't replace it. Similarly you can void your warranty if you flash the firmware of your DVD drive, in which case they wouldn't replace it.
Installing Linux on your laptop, however, does not void the warranty. It falls into the first category, along with getting new earbuds for your iPhone. Using your analogy, they support the combination, not the parts, so by that logic they won't replace your defective iPhone if you replaced your earbuds.