That doesn't sound right to me.
As of last year, the nationwide medical school acceptance rate was roughly 40-50%. If you assume a totally random process, then maybe you could say that acceptance is definite by the third try. But we know (or hope) that the process is not quite so random. This tells me that truly inadequate candidates would never get in, regardless of how many times they try; furthermore, truly qualified candidates will get in at first crack.
I don't see how it could ever take an average of three tries to get in. It's probably more realistic to say that a person who can't get in after three tries is not likely to be a good candidate without some extraordinary work.