Even worse than someone putting an AMG badge on a car is someone else worrying about it too much.
It is no different than adding custom wheels, pedals, floor mats, etc. Chill people.
After all, an M badge just means motosport. Equivalent to racing stickers you see in side windows. No big deal.
When someone puts a DINAN badge on the back does the whole car have to be DINAN or just at least one component?
BMW puts the M badge on several parts even though the car may not be an M3/5/6.