If you mod the engine and the tranny blows...
Of course it's not under warranty.
If the trans was manufactured to handle the hp and torque of the engine at factory spec, and you raised the spec, it's not their fault the tranny didn't hold up. Same with the differential.
As far as burden of proof, unless you're rich or a lawyer, you're gonna lose 99.999% of the time. No manufacturer thinks anything of spending $50k in legal fees to keep from paying your $5k warranty claim. They'll tie you up, in the meantime, you're paying notes and insurance on a vehicle you can't drive. If and when it does come to court, one miniscure boo boo on your part, and poof, you lose anyway. Most legitimate lwayers won't even take your case.