Yes, but I wonder if this has to do with the caliber of students or more to do with spots left?
Probably both. The students that are on their game and get everything done ASAP are likely the same kind of people that are generally on the ball and well-prepared. It would be unusual to be a slacker throughout your undergrad career and then all of a sudden step it up for medical school admissions.
At my institution, acceptances are essentially handed out to applicants based on a composite score following discussion by the various admissions committees. Applicants are essentially "ranked" by their scores, and applicants with higher scores receive acceptances. As you might imagine, this opens up the opportunity for applicants to be "bumped" down the list as the applicant pool fills out. This is by no means a strict rule, but hopefully it gives you a sense of how the process works at some schools and why applying early is advantageous. In fact, I remember Michigan releasing something a few years ago that essentially said that an overwhelming number of the students that are ultimately accepted submitted their application prior to September (something in the 70-80% range). The acceptance rate for students that submitted their application in October or later was abysmal.
This matters less for non-rolling schools, but even then you can speculate generally based on when you receive your interview invite. If you're complete in August and receive an interview invite early on, then you're likely a competitive applicant and stand a reasonable chance at getting accepted. If, on the other hand, you're complete in August but don't get an interview until much later on in the cycle (e.g., December), then you might guess that you're not as competitive - at least not competitive enough for the school to grant you an interview right away. By no means are you interviewing for the waitlist, but it gives you an idea of where you land generally on the "competitiveness" spectrum.
As far as getting interviews later on in the cycle and whether that means you have a real shot at getting accepted or not, my guess is that this is school-dependent. At my institution, enough slots are held until the interview season to ensure that all applicants are genuinely interviewing to be accepted. The number of slots and all that stuff is based on historical data; taken over years, the admissions office has a pretty good idea of how many applicants are likely to be strong and earn an acceptance, thus it isn't difficult to plan for that accordingly. I think it's pretty weak for a school to have students spend the time and money needed to come out and interview for what is effectively a spot on the waitlist, but it really wouldn't surprise me if that happened at the schools that interview large numbers of applicants and/or have many, many applicants (e.g., Georgetown, BU, etc.). However, I really don't know for sure, and, again, it likely varies from school to school.