Can white really not win this rook endgame?

Question

When playing against a player rated ~2500 Stockfish 8 managed merely to draw when playing white. This was the endgame before the draw (the draw occurred because it was king vs. king in the end).

Black played rook to h7 and then Stockfish played the rook to a7.

Answer 1

According to the Shredder database (sorry, I can't link directly to a position), the position after Rh7 is won in 32 moves and Ra7 gives the win away.

There are some similar positions with a- and b-pawns which are drawn, but this is not one of them. Actually, playing around with the database, I found that the initial position with the black king on b8, is drawn (and Rh7 is one of the two moves keeping the draw).

Another example is this one, where the white rook is tied to the defense of the b pawn and the white king can't really help.

[White "J. van der Wiel"]
[Black "P. Boersma"]
[Result "1/2"]
[FEN "8/2k5/1R6/PP5r/8/4K3/8/8 w - - 0 1"]

1. Ke4 Rh4+ 2. Kf5 Rh5+ 3. Kg6 Rc5 4. Kf7 Rh5 5. Rc6+ Kd7 6. a6 Rxb5 7. a7 Ra5 8. Re6 Kc7 1/2-1/2

_{source: Fundamental Chess Endings by Müller and Lamprecht}