<p>There are never really “equally qualified” applicants. Yes, all the top applicants have good stats, but after that, admission is about “fit” with the program, and some applicants simply fit better than others.</p>
<p>You’re trying to make one variable make a difference in your hypothetical scenario, and it won’t. </p>
<p>Here are some more variables:</p>
<p>What if the professor was hated by all and sundry in his graduate program or postdoc?
What if the professor writes the applicant a lukewarm letter?
What if the current faculty don’t know the professor at all? How would they know s/he was an alum?</p>
<p>See?</p>