I agree that the probabilities should be the same. And I don’t think it matters, whether one actually applied to the other school.
The issue is that we don’t know P(A) or P(B) (I’m using A and B to mean getting into the two schools), mostly because we don’t know all the factors that go into them. But if one of those were to happen, it is reasonable to assume that the probability of the other one happening is higher (than a more general initial assessment might have estimated).
This is like saying A and B don’t influence each other, but what goes into A and B are similar/related. Which again, is to say, that they’re not statistically indepedent.
One example that at first glance seems slightly unlikely proves absolutely nothing.