Win Or Draw?

HERE is an interesting rook-and-pawn ending from a super-tournament played in 2001 in the Kazakh capital Astana.

Black to make his 55th move in Shirov - Morozevich

"All rook endings are drawn" is a well-known aphorism by Tartakower, or was it Tarrasch? It certainly sounds more like the former to me.
Anyway, more to the point, is this endgame a win for White or a draw?
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55...Kb4?
This looks natural, but Black lost a second pawn after 56.Rb6+ Kc5 57.Rxh6, and eventually the game.
Later, according to IM Vladimir Barsky and GM Alexander Baburin, writing in the October 2001 edition of Chess Life, Morozevich was told by Ablai Mirzahmetov, president of the Kazakhstan Chess Federation, that children in the audience nearly screamed out the saving move 55...Rxh5! (this draws because 56.Ra5+ Kb4 57.Rxh5 is stalemate).
Morozevich apparently replied: "Next time they should scream louder."
Would I have done better than grandmaster Morozevich? Well, immodest as it may seem, I might well have done as a very similar idea occurred in my game against the Turkish player Burak Akguc (unrated at the time, but now 2120) at the 1997-8 Hastings Challengers'.

White has just played 49.Ke3xf4? in Akguc - Spanton (2065)

BA should have played 49.gxf4! as 49...Rxb4 50.Rxa7 Kxh4 wins for White after the only-move 51.Rh7+, according to the Nalimov endgame tablebase.
After the move played, 49.Kxf4?, the game finished:
49...Rxb4+ 50.Kf5 Rb5+ 51.Kf4
Or 51.Kf6 Rf5+! etc.
51...Rb4+ 52.Ke3 Rb3+ 53.Kf2 Rxf3+! ½–½