I've been reading these posts with interest. Yes, I am a RPT
[Registered Piano Technician] so I've been around pianos a bit,
although currently my "day job" is a museum curator and performing
arts center manager (and I'm tuning one of its pianos tomorrow!).

What we call "setting the pin" is actually a very complex process
involving the pin block, the pin, the string between the pin and the
upper bridge (on uprights, this is two segments; pin to pressure bar,
pressure bar to upper bridge), the speaking length, soundboard bridge
cap (between the two bridge pins, then to the plate anchor pin.  And
actually, for most strings you are also affecting the other half of
the string where it goes back through all those segments to the other
tuning pin.  Theoretically, the string doesn't move around the
terminating pin but, in practice, it does.  I'm not even mentioning
the duplex scales where there is another "bridge" to provide a harmonic
resonance section of the string.

So, "setting the pin" is attempting to equalize the string tension
across all those non-speaking lengths _and_ setting the pin.  The pin
twists slightly in the pin block as you turn it, and you want to remove
that twist so the tuning is stable.  Now is it any wonder pianos go out
of tune??  Oh yeah, the tension of the string on the pin bends it a
little, too.

I think the amazing thing is that pianos can stay in tune!

David Dewey