Given that I was the person who first raised the suggestions/questions related to the sample rate and bit depth of the audio, I decided to dig further into the manuals.
And given that most of the people on this forum are more interested in the MONTAGE and Genos than the PSR-E models, I restricted myself to the MONTAGE Owner's Manual and Genos Owner's Manual. I searched those manuals for "bit" and came up with the following hits:
MONTAGE Owner's Manual
Page 4:
"The MONTAGE is loaded with 5 GB (in 16-bit linear format) of preset Advanced Wave memory (AWM2)"
Page 41:
"Your performances on the MONTAGE can be recorded as WAV format (44.1-kHz, 24-bit, stereo) audio files to a USB flash memory device."
Page 63:
"Waveforms Preset: 5.67 GB (when converted to 16-bit linear format), User: 1.75 GB"
Genos Owner's Manual
Page 73:
"WAV....... 44.1 kHz sample rate, 16 bit resolution, stereo"
Page 90:
"Since it is saved in stereo WAV format of normal CD quality resolution (44.1kHz/16-bit) by default, it can be transmitted to and played on portable music players by using a computer."
Page 109:
"Use this connector to output digital signals via a coaxial (RCA-pin) cable. The digital signal format is CD/DAT (S/PDIF). This connector outputs a digital signal of 44.1 kHz/24 bit."
Page 123:
"Songs (Audio) | Format | Playback | WAV (44.1kHz, 16bit, stereo), MP3 (44.1kHz, 64/96/128/256/320kbps, stereo)"
"Songs (Audio) | Format | Recording | WAV (44.1kHz, 16bit, stereo)"
"Songs (Audio) | Format | Playback (Multi) | .aud (Genos original: 44.1 kHz sample rate, 16 bit resolution, stereo)"
"Songs (Audio) | Format | Recording (Multi) | .aud (Genos original: 44.1 kHz sample rate, 16 bit resolution, stereo)"
That still doesn't explicitly answer whether the MONTAGE transmits 16-bit audio or something higher (presumably 24-bit) over its USB-TO-HOST connection, but it does output 24-bit WAV audio over its USB-TO-DEVICE connection.
And the Genos does output 24-bit audio over its coaxial digital audio connection, but it apparently outputs 16-bit WAV audio over its USB-TO-DEVICE connection when recording to a USB flash drive-- except there's the curious inclusion of the words "by default" on page 90, which raises the question of whether the user can specify something other than the default?