While researching something else,Trent Lott's Vietnam draft deferments popped up on my screen. Turns out there's his version, and the Selective Service System's version. From the January, 1997 (Memphis) Commercial Appeal [available at lexis.com):

Sen. Lott's version:

''I was a little bit ahead of the Vietnam curve,'' says Lott. ''Very few of my classmates went to Vietnam, but it was the next year or two after that when they really did start.'' Lott says, ''I never had an actual deferment, as I recall. But I never got drafted. I went from whatever it was, 1-A (eligible for the draft) to whatever you got in those years when you got married.''
(our emphasis)

The Selective Service System's version:

Official records, though, indicate Lott did receive two types of deferments. The Selective Service System says Lott was classified 1-A, or eligible, on Oct. 20, 1960. But he received an educational deferment on Sept. 12, 1963, a year before what the Selective Service considers the 1964-72 Vietnam era. (The United States halted the draft in 1972 when the military became an all-volunteer force.)

...Lott returned to 1-A status from March 11 to Sept. 20, 1965 - a heavy Vietnam draft year. But his enrollment in law school qualified him for a graduate educational deferment. As Lott neared law school graduation, he received a 3-A hardship deferment on April 12, 1967. [Lew Brodsky, director of public and congressional affairs for the Selective Service System } said the 3-A was available to men who declared family hardships, ranging from a dependent parent to a child, or even one on the way, as was Lott's first child.

All of Lott's deferments were legitimate, so why didn't he acknowledge them?