Unsatisfactory explanation for Chess Mentor move

In the Chess Mentor course "Clever Escapes from Common Mating Attacks", lesson "Anticipate and Prevent", at the first move, 1. g4 is dismissed with "An interesting alternative! Although the problem is that this move is not going to do much to help White defend his king's fortress. Black's going to continue with 1...Qh3 followed by a strong ...h5 or ....Rh6 which White will find difficult to face."

Yet after 1...Qh3, 2. Kh1 followed by 3. Rg1 in the case of 2...h5 or 3. Bg1 in the case of 2. Rh6 is sufficient to parry Black's attack (as far as I can see).

This leaves me rather frustrated as it feels like it's saying my move is wrong not because it doesn't solve the problem, but because it's not the solution the author had in mind.