How old is your cousin? And how come he understands stuff like "nicks" and how to change nick if doesn't play any multiplayer (assuming , that he is a normie).
If i knew i had such person at home who can acess my pc and change nick to some admin name that he noticed earlier while i was playing, i wouldn't let him touch my system or the game at all. It's really wicked and unlikely for someone to do that, to remember an admin's nick that he saw long ago and then use that nick for "lulz" coz i sew no lulz there. It's not fun lol, unless he knew you'd get banned for it , which i think he didn't know coz you yourself didn't know that it will.
Anyway, story or not, it was really shameful to RDs being banned for nick faking (daffy and you) , and this had to be done to ensure no one takes these rulebreaks lightly.
I somehow still believe you're not that stupid to do something like this and then cover ot with such a crap story so maybe you're right but just for the future tip : accept it without mentioning the actual reason if it is unbelievable, it helps a lot and saves time. I too had such problems because of my brother and friends who play samp. I'd like to see input from other members.