Note that unless you manufacture the CPU yourself you still cannot be sure if there are no hidden backdoors. For example the ME could pretend it's really running your firmware but at the same time running some hidden code only delegating some operations to your code.
Even if the intentions are 100% legit, this is an operating system that you can not update (as frequently as your main operating system), and has many attack vectors.
Yes, it could pretend to run your firmware, but secretly load it's own, but it's actually quite hard to hide a 5mb (2mb min) piece of firmware in the chip. Research microchip decapping. You can clearly see the different regions of the chip.
But yes, it could be possible to hide a few x64 instructions, or circuits that could be manipulated. But running a remote control environment that can share your screen without your knowledge can only really be done clearly by running a large separate application stack alongside your main chip. (For now, who knows where we'll be in 5 to 10 years).
MINIX is a completely different OS than Linux, not a flavor of Linux.
“MINIX Linux” makes as much sense as “MacOS Linux”.
Intel ME just runs MINIX.