That is simply not true. It is not required. A cartridge connected to a single ended input sometimes will hum with the ground connected and sometimes without. Sometimes the ground connection makes no difference.
This is consistent with balanced operation: you may not always get hum when converting to SE. However there is a reason why nearly every turntable manufacturer has a 5 wire system rather than 4, to prevent ground loops (IOW the ground is not mixed with the signal- this implies that the minus output of the cartridge is actually the inverting output, and in balanced systems the inverting signal is often denoted by a minus sign).
Even BSRs and Garrards from the 60s and 70s are set up that way. As a result they can all be run balanced since the ground is not ground looped with the signal.
While it may be true that balanced equipment might have been used in the recording process, the groove in the disc is not balanced.
By that measure, neither is it single-ended! Once the sound is mechanically encoded, you have the same conundrum that you have with actual sound- it is neither SE or balanced- it simply is. It is the way we handle the sound, once it exists as an electrical signal, that makes all the difference (no pun intended :)