If you look at the verification thread, its been 3 days after the opening, and the queue has moved 10 minutes. In another words, the latest guy got verified submitted his app at 9:40AM. Is it possible that the first batch of 6/28 will only consist of people submitted their stuff on first day? Will they even make it through the first day?
My prediction was they would make it part way into those that submitted on June 11th.
Using SDN data, we see:
in 2010, 22 students submitted on day 1 and by day 6, 48 students had submitted
in 2011, 23 students submitted on day 1 and by day 6, 53 students had submitted
in 2012, 39 students submitted on day 1 and by day 6, 73 students had submitted
in 2013, 64 students submitted on day 1
I know SDN is a small population of the total applicant pool, but there was a six day delay this year and SDN is not far behind last year. Due to that six day delay, June 28th is only 18 days away from day one. Last year, by day 6 (June 10), it was taking up to 16 days to be verified... Hence my prediction for part way into June 11th this year for the June 28th 'cut-off'. Also, one should factor in loss of work done by the AAMC during those 6 days, and one could even conceivably predict that they wont even make it past day 1, like you said.
Note: I did not go looking past old verification threads for this data, I have excel sheets already made from last year that parsed those threads for me.
Edit: I said July 11, but obviously meant June 11 for my prediction