Donald Trump has not been truthful regarding his deferments or the draft. News groups researched this information and made it known to the public. Donald Trump should have been honest with the American people regarding his view on the military and the reasons he did not sign his draft card and was rejected for service. Being upfront from the start gains more trust from the American voters.
All politicians lie to some degree and so it would not surprise me that Donald Trump is lying about his military deferments. In addition to this claim, Donald Trump has made many contradictory statements over the past few months in his run for presidential office so it makes sense that he would lie about this issue to appeal to his conservative base.
I have no idea about his military deferments as I was not there when the alleged deferments took place. Would it surprise me? Not really, but I cannot, in good conscience, call someone a liar about something without being able to back up the accusation with indisputable and hard facts.
Donald Trump does note appear to be lying about his military deferments. He received four deferments for educational reasons and one for medical reasons. However, it was for bone spurs in his heel. This appears to be backed up by a recent New York Times article. Although he probably did what he could to get out of serving during the Vietnam War, it does not look like he lied to the American public.