Sure, for a martial art it's pretty safe - still in a different league from (say) bouldering or lifting, though!

And in solo sports, you can almost completely set your own safety budget, whereas in martial arts there's a large irreducible lump of danger from "the other person lacks the control to do something safely". The only other person I know in person who does BJJ who I didn't meet at BJJ is a brown belt, and just got a four-month leg injury during a routine rolling session; I myself am only just over a five-month chest injury that was probably from someone very heavy simply throwing himself down on top of me when I didn't react in time (obviously he shouldn't have done that, but I can't control what other people do).

Also how on earth are you managing not to get bruises at BJJ?! My legs are covered in them after pretty much every session just from sustained pressure.