Slight nitpick: the creature dying happens simultaneously with the counters canceling out. In this case it has the same effect as the way you describe it (has the same effect for persist or undying as if the death happened first) but there are a whole lot of state-based actions and sometimes it's relevant to note that any time multiple state-based actions need to be taken, they all happen as one event.

The reason those counters screw up persist and undying is that, while they're removed at the same time as the creature dies, once it dies and its ability resolves it's no longer a creature on the battlefield anyway, so it looks back in time to before it died to see if it had counters. Since "before it died" is also before the counters annihilated, it sees both +1/+1 counters and -1/-1 counters and neither persist nor undying would trigger.