A couple excerpts from wikipedia, if you want a more 'reputable' source there is this book which is excellent:
http://www.amazon.com/Piano-Servicing-Tuning-Rebuilding-Second/dp/1879511037
Basically this is saying what I said earlier. Since the harmonics on a piano are all sharp (this is inescapable) the tuner must compensate.
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(preceded by an equal temperament chart)
The tuning described by the above beating plan will give a good approximation of equal temperament across the range of the temperament octave. If it were extended further, however, the actual tuning of the instrument would become increasingly inaccurate. This is due to a factor known as inharmonicity, which is present in different amounts on all piano strings. The harmonic series of strings does not fall exactly into whole-number multiples of a fundamental frequency, but rather each harmonic is slightly sharper than a whole-number ratio, and this sharpness increases as higher tones in the harmonic series are reached. This means that an aurally tuned octave will be slightly wider than the just 2:1 ratio assumed above, known as a stretched octave. The amount of stretching depends on the style of piano and is determined mainly by the length of the strings: shorter pianos such as baby grands and spinets will have octaves that are stretched farther than concert grands.
This has the effect that, on a piano, the notes in the higher register will end up slightly sharper than those in the lower octave. This is less apparent on longer pianos which have proportionally thinner strings (string inharmonicity is directly related to the ratio of string thickness to length). Despite this deviation from the simpler ideal equal temperament, this is considered the correct way to tune a piano because it maintains interval identity across the piano, which generally improves the sound of music played on it.
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In tuning, the relationship between two notes (known musically as an interval) is determined by evaluating their common harmonics. For example, we say two notes are an octave apart when the fundamental frequency of the upper note exactly matches the second harmonic of the lower note. Theoretically, this means the fundamental frequency of the upper note is exactly twice that of the lower note, and we would assume that the second harmonic of the upper note will exactly match the fourth harmonic of the lower note.
On instruments strung with metal wire, however, neither of these assumptions is valid, and inharmonicity is the reason.
Inharmonicity refers to the difference between the theoretical and actual frequencies of the harmonics or overtones of a vibrating tine or string. The theoretical frequency of the second harmonic is twice the fundamental frequency, and of the third harmonic is three times the fundamental frequency, and so on. But on metal strings, tines, and reeds, the measured frequencies of those harmonics are slightly higher, and proportionately more so in the higher than in the lower harmonics. A digital emulation of these instruments must recreate this inharmonicity if it is to sound convincing.
