Neither. Because, as you said, rank has no real meaning outside the school/org that issues it. That could be the weakest BJJ in the world, and an Olympic gold medal winning Tae Kwon Do competitor.
True, knowing just their ranks doesn't give you enough information to necessarily distinguish between two practitioners. There are (just for an example) many, many TKD black belts out there who are much more accomplished martial artists than I am.
What the BJJ community is vociferous about is brand protection of a sort - making sure that any BJJ black belt from any school or organization can be expected to live up to certain (reasonably high) minimum standards. (Using myself again as an example - I'm a lot closer to the worst BJJ black belt in the world than I am to the best, but I'm still a reasonably competent martial artist.) Calling out fraudulent black belts is part of the brand protection process. I've seen several examples in this last year or so of fake BJJ black belts being called out (sometimes with the confrontation being captured on YouTube) and being publically humiliated and/or losing the teaching position they had gotten using their fraudulent credentials.
Right now, there's a bit of a furor in the online BJJ community over a couple of teenage girls who are running a school in Colorado. Apparently these girls had earned black belts in either Kajukenbo (or some Kajukenbo-derived hybrid art, it's unclear which) under their old instructor before said instructor went to prison for child molestation. Their parents bought the school when the old instructor was locked up and the girls took over as teachers. The girls then got blue belts from the Gracie University and went through instructor training so they could set up their school as a Gracie Certified Training Center where they teach both BJJ and whatever their hybrid striking art is.
This would be annoying enough to many BJJ folks, especially since they are competing with an established BJJ school that has multiple black belts, but at least some folks would be inclined to roll their eyes and move on. What really stirred an uproar is that the girls apparently decided that their striking art should use the same design of black belt that BJJ does. This design (with a red panel indicating instructor status on which stripes are added to denote degrees) is pretty unique to BJJ. I don't think I've seen it used in any other art.
Supposedly the girls wear their blue belts when teaching BJJ classes and their black belts when teaching their striking art. However pictures emerged of them wearing their BJJ-style black belts over their BJJ gis and this was widely interpreted as them claiming BJJ black belt rank. They've denied that was their intention, but there's been a big stink about it regardless.
I imagine that at some point down the line the battle may be lost and there will be enough fraudulent and/or substandard BJJ black belts that the rank will be meaningless unless you know the standards of the particular instructor/organization that promoted them, just as it is in most other martial arts. In the meantime, the brand protection process has succeeded to the extent that you can expect a certain minimum competence from any BJJ black belt, regardless of their lineage.