Here is where I read it at the bottom of page one.
http://www.drtube.com/datasheets/12ay7-rca1953.pdf
Tony
Ahhh... That 'splains it!
Right above this qoute is the basing diagram. When you operate with 6.3v, you use pins 4/5 (tied together) and pin 9. That is a humbucking filament connection. 12.6v wiring uses pin 4 on one side and pin 5 on the other; pin 9 remains unused. That is not "humbucking". So RCA wanted to cover themselves by suggesting the humbucking connection be used when you want the lowest possible hum.
Which doesn't really mean 12.6v will result in hum. But you will not be using this tube in a super-low-level signal stage anyway within a guitar amp. You might see super-low-level in something like a voltmeter for very small a.c. voltages (less than 1mV). When building something like that, the engineers (if the final meter price can justify it) will attack every possible hum source.
For example, Hewlett-Packard introduced a vacuum-tube meter which could measure very small d.c. voltages. A.C. hum might upset the circuits doing the measuring, so they regulated the power supply. 60Hz hum might still leak in and mess up the process, so they hit on an idea to convert the incoming d.c. to light, which was chopped mechanically at a rate that was unrelated to the line frequency or any harmonic of the line frequency (call it
a.c. light). Amplification of the small signal could happen of an electrical a.c. signal created from the chopper, then reconverted to d.c. at a higher level (relatively immune to noise). The reconversion Process responded only to the unique frequency created by the chopper, and strongly rejected any hum component or harmonic.
We have no call for such extreme measures in a guitar amp. And RCA's note is more targeted to those folks who might have cause to take such extremes.