Should I be concerned that my (successful) application to grad school only barely survived the first cut?
we were in the bottom of the pile.

Not really! You were in the very top of the pile. Many departments get more PhD applications than they can accept. Typical acceptance rates are about 10%, although I don't know about statistics specifically.
So if they offered eight spots, you were applicants #9 and #10. That's good. Unfortunately, when it comes down to choosing eight people out of the top 20 or so, it comes down basically chance. There is no objective way of measuring how good a candidate might be. So there is likely no real difference between #9 and #10, or more critically, between #8 -- the cutoff -- and #9. That a professor was asking for you specifically means a lot more than the overall ranking come up with by a committee.
Because &quot;ranking&quot; in the top 10% or so is meaningless, it doesn't really correlate with performance. Likely, you and you cohort study different enough things that it's hard to compare anyway.
It is quite inappropriate for a professor to reveal students' &quot;rankings,&quot; especially to other people, though.