Regardless of AMT there is standard protocol to remotely wake computers over ethernet (since mid-90's or so). NIC that supports it can be powered from 5Vsb and

Regardless of AMT there is standard protocol to remotely wake computers over ethernet (since mid-90's or so). NIC that supports it can be powered from 5Vsb and in that mode listens for specially formatted ethernet frame (format is somewhat configurable, but by default it consists of several repetitions of NIC's MAC in payload, actual destination MAC is unimportant as long as the frame passes through configured receive filters) which causes it to pull down wire going into motherboard's power management logic (and thus causing the same thing as pressing power button). This usually has to be enabled by BIOS and thus does not work in S0 (as is the case for almost all wakeup sources except physical power button, which is usually wired such that it unconditionally shorts PSU's PS_ON wire to ground and does not need any software configuration to cause wakeup). Probably all onboard NICs support this and for PCI cards this requires additional cable between NIC and motherboard, PCIe includes required wires as pins B10 and B11 (with 3.3V instead of 5V and with active detection that inserted card is actually capable of generating wakeup events). If I correctly understand how AMT works then it implements it's own mechanism with similar purpose inside ME firmware, which with AMT enabled remains active even in S5.