For the most part, in my understanding the academic year begins July 1st. that being said some programs are able to stretch it to the last week of June saying that they'll give a week off at the end of intern year or at the end of residency (making it up somehow... i'll believe it when i see it). The reason people are "starting" before that is because every program requires you to have certain training in order to begin working as a doctor. My program required us to be ACLS and ATLS certified, coupled with the mandatory GME training/orientation, we were required to report June 15th.
In my opinion most programs will understand a wedding or some significant life event and be able to work with you (i've seen people pay for ACLS and ATLS on their own, or take them while still a med student for free at their own programs in order to work around this for much more trivial reasons).
Basically, you should be able to work around things, in my opinion...
AS