WNW: I Cling to JIBE!

So saith Melanie J in a recent e-mail (and many others who have asked me about this one, as well as friends who try to correct one another).
Here's the issue: which is correct, JIBE or JIVE?
As in:
It doesn't JIBE with that.
It doesn't JIVE with that.
Hmm?
I've heard rather heated, adamant arguments both directions. When the question was posed to me some time ago, I wasn't sure. They both sounded right, and I could argue either.
So I turned to my handy-dandy research sources.
One of my faves, span