Agreed, the site is interesting, and it certainly illustrates that h+f endings are difficult!
The conjecture on this site that Jonathan Speelman's analyses in BCE of the
Gligoric-Smyslov position is wrong, is correct. However this was known for a very long time.
Smyslov himself anotated this position in his book "Rook Ending" and pointed out that Kh7 instead of Kf7 would lose. He should know, after all he had reason to study this position very carefully!
However the 'original'analysis that black could have saved the position after Kh7 is wrong as well.
This will become immediately apparent after studying the analysis of the endgame Keres-Sokolsky
in either Keres Practical Chess Endings or in Smyslov's book.
Furthermore the drawing method in the position with both pawns on the sixth rank is also flawed.
It's easy to see how to transpose from this position to a line in a study by Maizalis (1939).
The study is given in BCE, though the annotations by Keres are far more clear.
Finally the positions where black needs his king on h7 always involve an h-pawn on the sixth rank.
Indeed Keres warned his readers to leave the h-pawn as long as possible on the fifth rank to make
sure it was difficult to capture! And Smyslov played his king from f7 by g8 to h7 AFTER white had played h6!.
As an afterthought:
It won't be long untill we no longer have to consult endgame manuals for this position. Soon quite a few people will just jam a six-men tablebase DVD in their computer. Unfortunately you can't jam the same DVD into you head (at least not with positive results). So for those who want to understand HOW to play these endgames a good endgame manual and some studying will always be necessary.
And finally: the website cited above might scare people away from BCE and de rook endgame survivor guide. But in fact both are excellent books in their own categorie.
BCE has quite a lot of verbal explanation and 'rules' for an encyclopedia.
The rook endgame survivor guide has even more explanations, but of course is a monograph.