Instead of being cryptic, tell me what you disagree with?
dlockers has explained it
You're doing your weird thing where you mix up periods again. If he does nothing he makes the full amount.
If he does a BT he gets to make the money again less the 2% fee.
so to take your example, you make £1k for the first two years
it's only in year 3 that you need to factor in that 2% transfer fee if there is one
if you don't transfer, there's no fee...and you're still £1k richer
if you do transfer, then it's your savings rate vs your balance transfer rate, so if it's 4% savings vs 2% balance transfer, you're still 2% quids in