@sweelinck regarding tuning just a little sharp, that makes a lot of sense to me because as you tune, it affects the overall tension, which means usually when tuners finish, they have to go back to the start and adjust. This takes into account that progressive tension change. I bet a lot of tuners do this actually, and just don’t tell their clients they’re doing it (after all, the end result will be an in-tune piano). He probably just told @twocats because he could tell she would be paying attention.
My tuner is retired from working as the head tuner for the music school here, which has just under 500 pianos, including several very high end concert grands in four full sized concert halls.
As you can imagine, the experience of having taken care of so many pianos has not only made him an excellent tuner, but he has lots of tricks up his sleeve, as the saying goes.
He was telling me about tuning the concert grands. Because doctoral students have to do so many recitals, the concert halls are almost constantly in use and often there’s very little turn around time between recitals. The grands are kept under the stage directly beneath the stage's center, and when they’re used, there’s like a trap door there that gets opened and the piano is lifted straight up. So he would have to tune the piano under the stage, where the air is particular temperature. But then the piano lift is raised and the piano comes up to the stage, the stage lights are turned on and the temperature goes up just enough to impact the tuning.
He said he learned how to tune the under-stage pianos slightly out of tune (I think he said just a little sharp, but now I’m not remembering) so that when they’re raised up and the lights come on, the piano would be just in tune. He had to do it this way because he wouldn’t have time (or wouldn’t be allowed) to re-tune the piano in the time the piano gets raised up and the concert had to start. He also said this wouldn’t necessarily work on just any piano, but there were some S&S and a Fazioli that he knew well and could do it just right with.
And for the record, my piano’s tuning has always been pretty stable, but it has never better than since this gentleman took over its care.
So back to @twocats (sorry for the thread drift!) IMO the concern is not the technique used to get to the final tuning, but the actual tuning itself and whether it gets her piano sounding the way she wants it to sound.