Why does KQ vs. KP (flank pawn) on 7th draw? Silman mentions that King and Queen vs. King and pawn on the 7th rank wins, except when it's a flank or rook pawn (and the king is far away from the action, i.e. 6th rank).

The rook pawn case is clear; black king on h1 gets stalemating chances with its pawn on h2.

But the c-pawn and f-pawn case isn't clear to me. Why does King and Queen vs. King and flank pawn on the 7th rank draw?
For a similar reason, black also gets stalemating chances:

[FEN "8/8/1K6/8/5Q2/8/5p2/6k1 w KQkq - 0 1"]

1.Qg3+ Kh1! 2.Qf3 Kg1 3.Qg3+ Kh1 4.Qd3 Kg1 5.Qg3+ Kh1 6.Qxf2 {stalemate}


There are some ways to win if the king is close, but if it's far away as you say then white can't make progress -- he can't take the pawn without stalemating black.