Theoretical physics shows "irreducible complexity" arguments invalid.

[Angrboda]

Perhaps I'm misunderstanding something about chance, but what's the difference between a statistically extremely unlikely event happening and the possibility of such events being observed?

It's still a statistical probability, and no further reason would be required, other than for personal incredulity: Not unlike the possibility of life arising from inert matter.

No matter how remote, the possibility existed, and if life did arise in such a way, the remoteness of the probability has no bearing on the event having or have not occurred.

From the perspective of probability, the unlikeliness of an occurrence doesn't lead to a conclusion that it was impossible that it occurred. However, as a matter of science, when improbable events occur, and particularly if they repeatedly occur more frequently than chance would seem to indicate, there is reason to suspect that an unknown mechanism is altering the probabilities in unknown ways. Whatever that mechanism, finding it would provide a better explanation of events than simply that it "just happened." In one sense, natural laws are such explanations of improbable events. Before Newton's laws of gravity, it was known that the planets traveled in elliptical orbits, but not why. Not knowing the classical laws of gravity, it seems improbable that all the planets would adopt elliptical orbits "just by chance." So Newton went looking for the explanation for this improbable pattern of orbits. His law of gravity explained the improbability.