It's hard to tell without knowing more, but it sounds like there might be confusion in these podcasts between probability and statistics. Probability deals with predicting the possible outcomes of a single event. Statistics deals with analyzing the data from many events.

Quantum mechanics is, by its nature, probabilistic. Therefore, entanglement, which is a quantum phenomenon, is also probabilistic. It is not statistical, since it doesn't require you to account for a lot of events. In fact, in the simplest case, you can link 2 particles together via the laws of quantum mechanics and using only one event (measurement of one particle), you can write down the probabilities of later measurements of the second particle. That's probabilistic, but since it deals with only one pair of particles and 1 or 2 measurements, it's not statistical.