I also don't think you can't say that those who interview in September don't have a higher advantage than those in October.
Many schools operate on a rolling admissions basis, meaning the admissions criterion get a bit stiffer as the weeks go by.
Somebody who interviews in the beginning of September WOULD have a marked advantage over somebody interviewing towards the end of October, at schools that operate on rollling admissions.
Does that mean October applicants have no luck? Of course not, and such a broad statement on my part would be foolishness.