Same way you know if other probabilistic prediction systems are "wrong"

I asked about a single forecast, not about a prediction system (for which, of course, it's possible to come up with various metrics of accuracy, etc.). Can the forecast of 70% chance of rain tomorrow be wrong, without the quotes? How could you tell without access to the underlying forecasting system?

but my suspicion is that there's something going on that we haven't yet learned to predict

So your position is that reality is entirely deterministic, there is no "probability" at all in the territory?