Hey man, eight year vet here who has had a very successful application cycle. Through ten interviews I've been asked very little about my military experience except for how it shaped my motivation for medicine. If anyone were to ask about why you left the service the answer, "To pursue medicine" would likely suffice and talking about the circumstances of the discharge would be superfluous. Also realize, by even taking the oath of enlistment or commission you've made a commitment most people would never consider.
What would look suspicious is putting that you are a veteran on the application and never mentioning it, or leaving it off altogether and having unaccounted for time. Your definitely want admissions departments to know you are a veteran, it's a game changing status.
Concerning the "not fulfilling a commitment" chatter, it is baseless. I spent my last 2.5 years in command and discharged more than a few soldiers for body fat standards. They are very strict and for many age brackets unrealistic and encouraging of dangerous weight cutting behavior. It's often a very odd situation when it comes around to actually putting someone out.
Overall I'll share with you the best advice I received on the admissions cycle and interviews, "Don't be a spaz", put it on there and leave off the circumstances unless asked specifically, be proud of the service you did do.