As you said in your second sentence---Resumes get you in the door. Resumes are just as important,than the interview. A poorly constructed resume keeps you on the outside looking in. Rather you did or did not play a sport in college does not determine if you can do the said job you are applying for. BUT....if all else is equal, it sure can go a long ways. When I applied years a go for a job, the owner told me two things stuck out: My military service, and that I had played a sport(in college). So it helps, and it helps to list such things.
As you also stated, if you choke the interview..........Well, that's irrelevant to the discussion. If you "choke" an interview, odds are, the hiring employer isn't really going to care(resume). BUT, as the example I gave---IF you do not choke, nor does the other, and the employer decides to look back over said resumes. The fact that you played sports, was voted a captain, most certainly could be the swaying "vote" that gets you the nod.