Now that story rings true, as far as a believable voice behind the
words is concerned!  I'd vote for Eddie Cantor.  It's just too much
of a coincidence that this story says not only that he said it, but
that he said it to Rogers - yet, independently,  Rogers seems to have
gotten credit for it.  If the story is true, perhaps Rogers retold it
somewhere, and thereby got credit for the quote...or being the more
"quotable" person of the two, the story being told and retold, he
eventually received credit by association, so to speak.  In any case,
I feel relieved that Rogers might be freed from this possible stain
on his more wily rhetorical reputation.  Just an opinion, of course.

Ben