Got it -- courtesy of Amba Lee, who's something special in the way of researchers (and in other ways too).

The original "They Always Pick On Me" is by the great WWI-era vaudevillian songstress Ada Jones. If my memory didn't slip between there and here, I think the first date of the recording was 1911. The 78 rpm record (it may actually have been a cylinder) is filed at

http://ia300035.us.archive.org/0/items/AdaJones_part1/AdaJones-TheyAlwaysPickOnMe.mp3

Ada Jones is a treasure, one of the finest troupers of her day, successor to the turn-of-the-century tradition of Faye Templeton et al. Her repertoire had all sorts of comic songs in it as well as some standards. I've known a few of her other songs for years -- I heard "He Lost Her in the Subway" in 1959 and it's been in my repertoire ever since.

Obviously this is where Helen Kane got the song for Betty Boop. Indeed Jones' style may have given Kane the idea.

The Jones recording may also be where everyone's great-grandparents got it, although Boop could as easily be your grandparents' source.

Since the Ada Jones version is available and hearable, I won't ABC it -- go to the site, folks, and treat yourselves! An early recording-era classic.

Bob