My daughter sent me this
link. I don't know where it came from, but it sounds as though it's soloed vocal tracks from the original (or more likely, the recently-digitized) multitracks. You can even hear the headphone bleed, and sometimes the instruments that were being played simultaneously with the vocal, e.g. McCartney playing piano while singing Mean Mr. Mustard.
Keep in mind while listening to these a capela snippits that they predate Autotune by three decades. The only tricks here are double-tracking, reverb and tape delay. And, I assume, the Fairchild 670 they were fond of on everything.