If it can be done on exe's at runtime, it can be done on hardware attached to the computer. Signing things securely isn't a hard problem to solve, it's keeping people from attacking that signature that is hard. Something tells me the kids writing lua scripts as aimbots aren't quite smart enough to crack a proper signature implementation.
This is making me feel old. Totally agree it is difficult, but not impossible.
Logitech is the problem here for even allowing this in the first place. No CRC checks for mouse firmware or anything? It screams poor implementation. I will not be surprised if anti-cheat software starts banning people or companies like Logitech.
Kind of sad to see the number of threads and communities online encouraging this. The point of games is to have fun, when you cheat all that goes out the door.