Ah, that is precisely what went wrong in the original study! The author (and the solvers no doubt) trusted their intuition on the final position and it turned out to be wrong. Probably the most important spin off of TB is that it forced people to retrain their intuitions because so often things proved different.
I agree though that the fight against B+2 pawns is probably not that hard. I doubted that solvers would find a line that would force the win of the 3rd pawn!
The solver can use his intuition here like I did, usually Q wins against such material, Pa2 is creating a constraint on the WK but finally one can understand that zz kills B hopes after g7 is lost (with g5 played I would not be that sure). White is supposed to be the perfect Chess players...