These "one-day-short" duty tours are a formal program; it's unlikely that
anyone can sneak an extra day in just to get benefits. They're implemented
usually during transitional periods when military needs are uncertain. They
would accept applicants, even draft people in large numbers, in case needs
increased, then decide near the end of training whether they needed to keep
them. If needs kept dropping, they were ushered out a day short of the
government's obligation for further benefits. The military benefits because
they have a large group of trainees in the pipeline in case needs surge, yet
their investment is bounded and the pipeline is easily emptied if needs drop
off. Many trainees benefit because they get to try out the military with
reduced chance of obligation to 2-3-4 years. The 1968 draft was about as big
as it got -- my August entry group was the Air Force's biggest-ever. But
just a year or so later the AF released hundreds or thousands of new officer
trainees a day short of commission (and mutual obligation) because Viet Nam
manning needs had peaked. The ones who wanted to go were disappointed; the
unwilling draftees who were drafted, got trained, then got to go home rather
than off to war were ecstatic.

Another example of managing obligations is a friend who volunteered --  
DEMANDED -- to become an infantry officer in Viet Nam. He served, got shot,
and was given two choices:
1. Get treated, heal, leave the military, and sign papers absolving the
government of all long-term responsibilities except those associated
directly with his wounds, or
2. Get treated, heal, and go back into combat.

Those are very fair choices, IMO. (He chose Door #1, because had seen enough
by then; he served virtually shoulder-to-shoulder with Lt. Calley around My
Lai.)

I.P.