Merestil: Not true. If the counter is not there, it is not there; if the creature is killed well after a +1/+1 counter and -1/-1 counter remove each other, then it will return. There is not an invisible -1/-1 counter on the creature to stop Persist from triggering; there is no -1/-1 counter at all at this point.
I think Ecoris has cleared it up, but just to be sure you understand.
I was answering three questions, because I was not sure exactly what the OP meant.
The third and last was "If a creature with +1/+1 counters gets -1/-1 counters and is put into the graveyardas a result of those -1/-1 counters being placed, do they stop Persist from triggering?" The answer is yes they do.
This is because all SBEs are processed as a single event; therefore when the game checks the gamestate just before the event (the SBE check) for triggers, it sees the Persistent creature has -1/-1 counters, and Persist does not trigger.