The answer to that is yes, but not for the reason that you think.
The average program goes down 6.5 spots on it's rank list for every spot they have. That means a program with 10 spots who interviews 100 applicants will, on average, fill the 10th spot with the applicant ranked #65. Why do they interview the other 35 applicants? Because half of the programs in this country will go further down their list than average and programs would like to have a buffer. So if you're ranked 35th percentile or higher, you're likely to match.
If it was completely random where in the distribution of the rank list any individual applicant would fall, having 10 interviews would give you a 1-0.35^10 chance of matching, or 99.99%. Hell, three interviews would give you a 95% chance of matching. But of course, it is NOT completely random where applicants fall. Some weak applicants who apply to reach programs and squeak by to get an interview might consistently be ranked near the bottom of the respective programs rank lists. Perhaps some applicants don't interview well. Or whatever else.
Look at the charting outcomes data and you see pretty clearly that throughout the distribution, people are matching somewhat less often than you would assume if ranking were random. Once you get to about 7-8 interviews, it gets to almost 100% match rate and anyone who didn't match probably had a pretty specific reason they didn't. So does your chance of matching approach 1? Sure. But you don't care about the population of people with X number of interviews. You only care about n=1. If you are an incredibly awkward person, you might be one of the 4 unlucky souls who did not match IM even with >15 interviews last year. So you still have to try.
