On some ThinkPad models, there is a chip associated with the LAN management engine (AMT) that should be disabled as well. This isn't the Management Engine controller itself, only has a power management role for AMT & WoL that cannot normally be disabled.
My ThinkPad has a physical switch for Wifi and Bluetooth, although apparently that is only window dressing and can be bypassed with a BIOS setting (& configuration tool from Lenovo)
What do you think of having a hardware firewall processor for the Wifi and Ethernet interfaces on security focused laptops?