When a real (wood&string) piano goes out of tune, it usually goes out of tune with itself also.
In other words, tuning the recording to make middle C in tune will move other recorded notes just as much, but they may still be off from each other. Actually pretty likely.
It's very rare a piano goes out of tune on every note in even amounts.
Just something to consider in your decision.
If it's out of tune with itself that's pretty hard to correct with all the overtones and such that exist on a real piano recording.
Piano's are not single strings for a note. Some of the low ones are, but as you move up you are playing 3 strings for each note struck. That's what gives a real piano it's timber and tone quality. You run into tuning problems, especially when the 3 strings per note are out of tune with each other.
Just think back to the sound you hear from the old western saloon pianos. (or the ones in the recreation rooms in many rest homes)