a.) Whether the computer can record datalogs or not is a moot point now. Even if they dropped the 5k/clutch dump line as bait to gauge your reaction, you're still fucked now. They expect damage to crop up. If I were the service writer, I would.
b.) It makes no sense to claim a 5k clutch dump damaged a synchro. The synchros match shaft speeds, not gear-loads when torque is applied to the shaft. Technically whether or not you sidestep the clutch makes no difference to the synchro. It only cares whether or not you engage that gear. It would be the same as saying "We aren't looking for whether or not you actually launched at 5k, we only care whether or not you selected first gear at that RPM." Tooth or shaft damage is another story. I could understand doing aggressive downshifts, forcing it into gear and powershifting the transmission, but a launch? The clues don't add up, batman.
c.) Be honest. If you were abusing the tranny and it's acting nasty, they aren't going to cover it. A fluid change with something expensive and nice wouldn't hurt and might actually help the grinding if it's not too far gone. If little metal bits come out, then you know you're fucked. It would be an outstanding opportunity for you to learn how to disassemble a 5mt and replace synchros. Perhaps a stronger gearset would be in order as well, if abuse was the culprit of the synchros dying.