AMT runs below the OS on a coprocessor inside the intel chip that has a privilege level greater than hypervisor to your machine and monitors the mobo ethernet independently of the OS. It can re-image and control your machine no matter what OS is running. Yes you're vulnerable running Linux.

Core 2 systems are not exploitable. It's only for Nehalem and later. Yes, you're also vulnerable on Linux.

> So if you setup AMT in the BIOS and run Linux you are exploitable?

Perhaps I misunderstand the question, but AMT is not dependent on the system's OS, by design. AMT runs on Intel Management Engine, a platform on the computer with its own CPU, memory, OS, bus, caches, etc. ... and applications, including AMT. AMT is designed to be used when there is no functioning OS.

Think of it this way: You paid for one computer, but you got two!