I get what your saying @ I see how I may have done the incorrect reversal of your statement. But sounds like a circular reasoning to me a bit.

So they rise in rank because they are selective. Wouldn't that mean that their selectivity is correlated with higher rank?

For example, if Harvard is ranked number 2 this year and they start selecting less students then by next year their ranking can go higher. That's essentially same as their selectivity correlated with higher ranking. And ranking correlated wiyh higher selectivity.

I don't want to say it's a causation because their ranking does also factor in other interesting elements.