Did Capablanca See What the Engine Sees?

Before I get to the first post in More Capablanca, a position flagged as one of Capablanca's Games 'To be studied very carefully', I have one digression to get out of the way. In the diagrammed position, White played 22.g4. Analysis by Nimzovich, copied by Chernev in 'Capablanca's Best Chess Endings', concluded that White missed a win with 22.Nf5 hxg3 23.hxg3 Bxf5 24.exf5 Ne7 25.Kg2 Kg7 26.Kxh3 Rh8+ 27.Kg2 Qh6 28.Kf2 Qh2+ 29.Ng2 Rh3 30.Ke1 Rxg3 31.Ne3.

New York 1913
Capablanca, J.R.

Kline, Harry
After 21...h5-h4

The machine comes to a different conclusion after 22.Nf5 hxg3 23.hxg3 Bxf5 24.exf5 Ne7 25.Kg2, and now instead of 25...Kg7, Black plays 25...Nd5, threatening a family fork on e3. The point is that if 26.Qd2, Black has the sacrificial variation 26...Nhf4+ 27.gxf4 Nxf4+, when 28.Kg3 (28.Kf2 is similar) gives Black at least a draw with 28...Rad8.

One line is 29.Rd1 Qh8 30.Qh2 Qxh2+ 31.Kxh2 Kg7 32.Kg1 Rh8 33.Bc2 Nh3+ 34.Kg2 Nf4+ with perpetual check. The move 29...Qh8 is hardly forced, as Black has more speculative moves like 29...Kg7, 29...e4, and 29...c5. I wasn't able to work through all of the complications in the time I had available, but I found nothing where Black was in any danger of losing.

Calculation or intuition: did Capablanca see what the engine sees? To play through the complete game, including the analysis by Nimzovich, see...

N Kline vs Jose Raul Capablanca; New York 1913
http://www.chessgames.com/perl/chessgame?gid=1261977

...on Chessgames.com.