Mark, if you're willing to fund the study, I'll do the work!
I honestly don't know EXACTLY what happens at the chemical level, but my own observations make me think the vinegar is interfering with the bonds between the clay particles, rather than reacting with the sodium or calcium. When used in repairs on bone dry clay, the vinegar works better than regular water because the repair is less likely to re-crack as the slip shrinks. Its not perfect, just better than water! Mostly I use a tiny bit of vinegar to soften the two edges, then make slip to stick the pieces together. The vinegar on the surfaces gives you more time to get the pieces in position and stuck together.
I had a batch of home grown clay from my yard that just would NOT settle and it was giving me fits. I mean over a week later it was still totally suspended in the bucket, sand and all, even though I had enough water in there that it was almost milk thick. I really wanted that sand out of there, and somewhere found a reference to vinegar as a flocculant, so I started adding just to see what happened. Sure enough, within minutes of adding about a cup of vinegar to a 5 gallon bucket of muck, the sand settled out and I could pour off the USABLE stuff. A couple days later I had wedgable clay. The stuff worked up wonderfully after that, nice and plastic, great for hand-building, and matured at cone five a very nice brick color. Right now I'm having fits because they're doing construction in the next lot over and they've scraped all the surface soil off revealing a BEAUTIFUL layer of pale gray clay. Its still has sand and small rocks in it, but its got far FAR fewer impurities than the lumps I was finding in the flower bed. I've been plotting a raid, but they've got the place fenced off so maybe not.