Something I think is relevant here: Everyone, including people who'd be expected to know, is saying that medical schools aren't looking at applications until either July 6th or July 15th. If this is the case, I think that a lot of this "must submit on June 1st to have a chance" talk is ridiculous. Keep in mind, guys, that it's much easier to deal with being rejected by a school when you tell yourself it was because you applied late.
I'm not saying it doesn't make a difference when you apply; I'm sure that it does. But I submitted my application today, and assuming it's verified by mid July, when schools can first supposedly see it, I'm not so sure the June 1st people have much of an advantage over me.
Don't be thrown into discouragement or into a panic, as I was when I first read some of this crap three weeks ago.