The Management Engine, think of it as running at Ring -1. It can access hardware below the level of the processor. Injecting malware into it would be the holy grail for attackers, it would be impossible for anything running on the CPU to detect it and the malware would have access to all of the low level hardware. It can even intercept or create packets on the network interfaces.

Luckily the implementation is obscure so it has perfect security, right? There's no way such a complex piece of software that has had very little oversight could have exploitable bugs that would completely destroy any security foundations you have on your machine.