Some people might find their middle name embarrassing, thus choosing to use an initial to keep it secret where it isn't required for anything but disambiguation.
When the middle name avoids confusion with another person and the situation is medical files its about as important as it gets. There is also a legal obligation for it to be accurate with some if our government contract work. That said, they don't seem to monitor accuracy. I spent a lot of time monitoring it though (checking, correcting, hounding data entry inaccuracy serial offenders), and it still causes me cold sweats every now and again.