DJ services is somewhat of a sidelight in my line of business. Any good DJ service should know that things sometimes run over and try to avoid scheduling things back to back where there could be a conflict.
We also have extensive questionnaires that include the question: "Do you anticipate this may run longer?"
Good DJ services also allow for extra time between gigs if they're going to schedule consecutive events. You not only have this issue to deal with, but the potential for breakdowns, equipment trouble, whatever.
A good DJ service also has the ability to provide a backup to deal with these kinds of situations. If he got held over and was offered double pay to stay, then he most surely could have stayed and called in a backup.
The concerns expressed by jeneisen are legitimate in regard to the company she referenced, and certainly not worthy of criticism.