Like I said, they're not dependent on each other, they're dependent on the same thing.

I hate to sound like but Bayes' theorem is really all you need here: in statistics those 2 things have the same effect on the probabilities. I agree with you that there isn't a causal relationship between the outcomes in each race and the causal relationship is to the voter preferences upstream in the chain of causality, but P(Rs winning House|Rs win presidency) > P(Rs winning presidency) regardless of what causes what.