I also agree, most of us in admissions know that prehealth institutional letters often will arrive later in August or September. My own analysis on this issue with one of my committees shows that our group did not adversely penalize those whose letters came later vs. those that came earlier.
That said, there are some adcoms that like to upset the prehealth advising community by imposing rather improper deadlines (before mid-July???!!!) on when they want those letter packets to be received. If there is anything you should learn about academia is that you can never impose a deadline on faculty unless you are offering a grant.
Unless you consider the penalty an adverse impact on students. Committees that prioritize their schedules over their students apparently do not.
Med school admissions really are a rat race today, and it is EXTREMELY SELFISH for committees to screw around with these letters all summer when admissions are rolling, there are more than two applicants for every seat, and the process begins more than two months before some of them get off their a$$es and push the letters out the door (end of June to end of August, or beyond). These letters should all be done, everywhere, by the end of May for people who make timely requests, if summer vacations are important. Otherwise, they should all be done before first AMCAS transmissions to schools take place at the end of June. Period.
No matter what anyone says, some people are absolutely adversely impacted by having to wait all summer before having their application reviewed by an adcom for no reason other than a committee doesn't want its summer vacation disturbed by the med school admissions process. Even if the polling of one of your committees indicates that they do not make any II decisions until all committee letters are received from all schools, which I am pretty sure would be absolutely BS, if anyone actually said that.
They are giving the PC answer to not ruffle any feathers, but any applicant who hustled to be complete early to be eligible for every possibly advantage in the rolling admission process should not have that taken away from them by a committee, or have to rely on hollow assurances from adcoms responding to inquiries from people like you that everyone has an equal shot right up until the last II is issued, because common sense dictates that is not true, anywhere.
Even though there are certainly spots available until there aren't, people who go to the adcom first have an advantage. I did far better with my earlier interviews than my later ones last cycle, and doubt I would have had as many interviews as I had if I was complete two months later than I was.