World Championship Lost

In No Best Move?, I learned that Lasker never had a lost position in the last game against Schlechter. Here I see that he shouldn't have won either.

In the diagrammed position Schlechter played 39...Qh1+. The game continued 40.Rf1 Qh4+ 41.Kd2 Rxf1 42.Qxf1 Qxd4+. Despite the small material advantage for White and reduced number of Pawn, Lasker won by trading his Knight for the Bishop, winning the a-Pawn, and trading Queens. A tablebase says that the R+P vs. N+P endgame will be mate after at most 28 moves. Kasparov pointed out a position on the 51st move where Schlechter had a better chance of holding the draw, but he missed the chance.

World Championship Match (g.10)
Berlin 1910
Schlechter, Carl

Lasker, Emanuel
(After 39.Kf2-e1)
[FEN "2R2b1k/p3p3/8/1n6/N2P1r2/P2Q1R2/7q/4K3 b - - 0 39"]

The right move was 39...Qh4+. Black either gets a perpetual check on the first and second ranks or picks off the Rc8 on a fork. An example line is 40.Kd2 Qh2+ 41.Ke3 Rxf3+ 42.Kxf3 Qh3+ 43.Ke2 Qxc8. Schlechter explained that his 35th move was the result of a miscalculation. Did he also miscalculate on the 39th?

His silence on the error led to speculation that he needed to win the ten game match by two games to win the title. I wonder who started the speculation.