Not personally being there, but only having my ears (which I trust
more than any other organ), I would say a variety of methods were used,
not just "one way" of recording a number.

For example, we all know that many so-called "hand-played" reproducing
piano rolls were actually a creative collaboration between a pianist
physically playing in the work, and then a very accurate and musically
literate editor going over the product away from a keyboard by
"reading" the roll and making alterations and touch-ups, the composite
being sold to the public as "hand played by such and such" and
sometimes the editor is actually mentioned.

A true transcription was often entirely prepared at the composing
drum without so much as a piano keyboard in the room -- note for note,
from the written score.

The only truly 100 percent hand-played reproducing piano rolls
I know of are those marvelous red paper Welte-Mignon gems, where
mistakes resulting from overt displays of ungirdled neo-romanticism
are reverently preserved due to the styles of the recording pianists
(artistic legends such as Richard Strauss, Claude Debussy and Gustav
Mahler, to name but three).  To eliminate them, as their American
counterparts would do, would be unthinkable and artistically
undesirable.

I would imagine that recording pianists worked both from memory
(certain black jazz and blues artists demonstrate this) as well as
by playing from a notated "score" which more times than not served
as a point of musical departure -- in reality, an arrangement of what
they considered a transcription.  Then the roll editors would throw
in their 2 cents worth for a finished product that everyone was happy
with -- or at least were convinced of the commercial sales potential
of their endeavor!

Stephen K Goodman - Professional Player Piano & Nickelodeon Restoration
Tarpey Village (Fresno/Clovis) California, USA
http://www.mechanicalmusicrestoration.com/