I am certainly no expert either, but maybe your piano tuner was referring to the practice of "stretching" an octave: The tuning described by the above beating

I am certainly no expert either, but maybe your piano tuner was referring to the practice of "stretching" an octave: The tuning described by the above beating plan provides a good approximation of equal temperament across the range of the temperament octave. If extended further, however, the actual tuning of the instrument becomes increasingly inaccurate because of inharmonicity, which causes harmonics to run slightly sharp, as increasingly higher tones in the harmonic series are reached. This problem is mitigated by "stretching" the octaves as one tunes above (and to an extent below) the temperament region. When octaves are stretched, they are tuned, not to the lowest coincidental overtone (second partial) of the note below, but to a higher one (often the 4th partial). This widens all intervals equally, thereby maintaining intervallic and tonal consistency. https://en.wikipedia.org/wiki/Piano_tuning#Stretch https://en.wikipedia.org/wiki/Piano_tuning#Stretch