who eats pumpkins?

There is an ongoing (and surprisingly frequent) makhloqet between Oren and me regarding the appropriate beginning to the phrase "_______, _______, pumpkin eater."
Oren says "cheater, cheater, pumpkin eater."
I counter that it is Peter who eats pumpkins, and the poem goes:

Peter Peter pumpkin eater
had a wife and (but?) couldn't keep 'er
put her in a pumpkin shell
and there he kept her very well.

I know I am right. Or rather, that my version is older/"original" and his version is derived, since mine has a whole poem, and his is just an accusation, but anyway, today someone else said his version independently. Both Oren and the second offender are children of immigrants, whose innauguration into childhood rhymes is apparently lacking. However, the question remains. What is the word on the street? Has "Peter" evolved into "cheater" for the youth of today (due perhaps both to their lack of familiarity with poetry and to the objectionable content of this particular poem...)?