Alright, allow me to go full-on music theory/jargony nerd here for a sec.
As an experiment, I threw the recording into Audacity and transposed it up one semitone (half-step) just to see how it sounded. I realized that, at least to my ear, it actually transposed up almost an entire whole step. The original is in the key of F, and the supposedly "semitone"-transposed version is actually more in the key of G than it is in F sharp. Now I should mention that, to my ear, it sounded more like a semitone and a half - so somewhere in between F sharp and G. Anyway, this leads me to believe that the original recording is actually about 50 or 60 cents sharp... which actually isn't uncommon for records like this. So, using this logic, the original is somewhere between F and F sharp, but to me, it sounds like it's in F. But this is one of those times where I'm not fully trusting my ear. I guess the test to see if this is actually true would be to go on a (in-tune) piano or some MIDI patch or something and play along with it. I'll have to try that!
EDIT: I should mention that transposing it up 0.5 semitones in Audacity produces a result that sounds a LOT more like F sharp to me. Again, "1 semitone" sounds like F sharp plus a little bit (or G and a little bit flat) - somewhere in between.
EDIT #2: I don't believe this is a bug or fault with Audacity. Again, it's common for recordings like this to have this quality.
