PTS#8: Pianos and mallot instruments cannot be adjusted.

Piano Thirds (& Sixths) are "fixed" and cannot be adjusted in keyboards and mallet instruments.

Crescent Noon (Moon) - The Frank Pooler Sound - Carpenters Sound

The choral and orchestra musicians compensate for the piano 3rds and 6ths.
As the piano plays 4ths and 3rds the 3rds have 7 vibrations a second and the 4ths are (almost) open.

If you listen to the piano in the example above you might be able to hear the vibrations of the chords of the piano. This is a normal sound that we are used to. But when the choir backs up the sound they adjust to their close approximation of the piano general tuning and then they tune to each other to make the chords open. Sometimes the choral performers are trying to adjust to the piano too much instead each other and vibrations occur. Some chords don't work all together, especially on the low alto notes.
Pianos are difficult to tune to.
This is a good example of the problem.

PTS#9: Pianos are stretched in the high end.

Each octave (for the piano) is sharper and sharper on purpose. This is called stretching the octaves. It is a standard procedure worldwide. Piano tuner software has this sharpness programmed into it. This is all common knowledge to piano tuners. Without the higher pitch high notes the top note of an arpeggio sounds flat. It has something to do with the process of hitting the string with a mallot.

“Pentatonix "White Winter Hymnal”

A Cappella singing is easier to tune with eachother.

PTS#10: Pianos are stretched in the low end by some tuners.

This is called stretching the otaves, but in the lower end.

The same thing is done regularly for the high end to make the top notes sound correct, even though they are a bit sharp. It has something to do with the short strings being hit with a hammer and not bowed like a violin.

When a piano play a arpegio and ends on a high note it should sound in tune when in actuality is is a bit sharp.

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