"Brain health," as it's used in this article, would also contribute to coordination, muscle control, and various other things that would benefit athletes in ways that are totally opaque to you or me.
The article doesn't say exercise makes you smarter, and even if it did, "smarter" is an awfully vague term.
Also - it's a very small sample size. And if I look more broadly... 2 of the seemingly "dumbest jocks" I knew in college went on to become doctors, one at the Mayo clinic. So perhaps their intelligence was showing in other areas until they got out of school.
This can happen for a variety of reasons: poverty, nutrition, "misaligned" interests, etc.
Intelligence plays a role in that someone with an IQ of 80 probably isn't going to Stanford, but there are ostensibly plenty of people with IQs far above your average Stanford student who will never set foot in a university.
If artistic ability has a strong influence on intelligence compared to athleticism, then P(intelligent | artistic) >= P(intelligent | athletic). We know that P(athletic) > P(artistic) from the data.
By Bayes' theorem:
P(intelligent | artistic) = P(artistic | intelligent) * P(intelligent) / P(artistic).
P(intelligent | athletic) = P(athletic | intelligent) * P(intelligent) / P(athletic).
Ignoring P(intelligent) for a sec, we find
P(intelligent | artistic) ~ P(artistic | intelligent) / P(artistic)
P(intelligent | athletic) ~ P(athletic | intelligent) / P(athletic)
If we accept the assumption that artistic ability is a bigger influence, then
P(artistic | intelligent) / P(artistic) > P(athletic | intelligent) / P(athletic)
Because P(athletic) > P(artistic),
P(artistic | intelligent) > P(artistic) * P(athletic | intelligent) / P(athletic)
P(artistic)/P(athletic) must be less than 1, so we get
P(artistic | intelligent) > P(athletic | intelligent)
I'm not really sure where I was headed with this, but it was neat to think about. If anyone spots an error please just correct me.