Since the real question is about authenticity and the salad has been around since, what, the dawn of time? it seems unlikely that there is only one vinegar that can be used. Unless the folks on Capri only had access to balsamic vinegar (seems unlikely -- I'm guessing they had all types of wine "spoil" just like everyone else, allowing an assortment of vinegars) it seems very inplausible. Not sure you'll find a food historian who can answer this question definitively, so, in the meantime, I'm voting with you. ;)

The "purest" caprese salad only has olive oil, moz. cheese, tomato and basil. Balsamic is the most common vinegar added.

Your friend is wrong, even if Joy is truly not a great source for Italian cooking. (Look to Marcella Hazan for that.) A real insalata caprese would not have aceto balsamico (balsamic vinegar) and most certainly not aceto balsamico tradizionale di Modena (the real, honest-to-god thing). Why? Because, first of all, the made-up aceto balsamico--usually a red wine vinegar to which some caramel may have been added for sweetness--is not considered a "good" thing in Italy, even though it is more widely used than it used to be. As for the real thing, you would NEVER (and if I could underline that word I would) use it on any kind of salad. It is much too precious (and expensive) for that. Beyond which, it is strictly associated with the Po region around Modena and Reggio Emilia and not elsewhere, and Italians still treasure the regionality of their food traditions.
If you think your caprese salad needs a bit of acid, and it might, use a good quality aged red wine vinegar--but just a small amount. When I'm writing recipes I often have to stipulate "vinegar, but not balsamic" in order to get the right flavor. Red wine vinegar can be a miraculous product--and even more useful than any whatever "balsamic."

I think if you like great balsamic vinegar, then use it. But nothing should take away from incredible heirloom tomato flavor.

In an untraditional way I like unseasoned rice wine vinegar.

Thanks for all the feedback, guys! Always good to know you're right on something. I have to admit - I'm not a fan of balsamic vinegar (or at least what I've had - maybe it wasn't a very good example?) so I'm perfectly happy leaving the stuff off my caprese.