I have yet to be convinced that there's anything inherently wrong with doing partial-volume mashing with BIAB. I also see no reason you couldn't do a partial boil for BIAB just as well as you could for extract or traditional all-grain, with top-off water post-boil.
Personally, in my last two batches I mashed a little thicker than full-volume and did some simple sparging - the first time I just poured 172 degree water over the lifted grains and the second time a small hot-water pour and a cold-water dunk that made squeezing the bag much easier. I've got an IIPA coming up sometime in the nearish future, and if I go for a full five gallon batch, I'll definitely be mashing thick.
I believe the roots of BIAB are full-volume mash and no sparge or top-off, but there's no reason to limit yourself to that definition if you have a good reason to do so.