Note, I'm not making any judgement on the person you are referring to (the Vietnam era veteran) in giving this answer. This answer refers to saying something which is technically true but may mislead.
The definitions generally seem to go something like "the use of equivocal language, or the act of equivocating", so I'll give the meaning of equivocal.
1. capable of varying interpretations; ambiguous
2. deliberately misleading or vague; evasive
3. of doubtful character or sincerity; dubious
1a : subject to two or more interpretations and usually used to
mislead or confuse
1.allowing the possibility of several different meanings, as a word or phrase, especially with intent to deceive or misguide; susceptible of
double interpretation; deliberately ambiguous:
Note that many dictionaries, such as Oxford Living Dictionaries only mention statements possible to different interpretations, but don't specifically mention misleading:
1.Open to more than one interpretation; ambiguous.
Oxford Living Dictionaries
Some people use the term half-truth for this.
A statement, especially one intended to deceive, that
omits some of the facts necessary for a full description or
American Heritage Dictionary
But I don't like this term. I think most dictionaries define is as only partly true. However the Wikipedia article states:
The statement might be partly true, the statement may be totally true but only part of the whole truth...
An example given in the article:
After being stopped for drunk driving, the inebriated driver proclaims
"I only had a couple of beers" in slurred speech. The driver may have
also consumed alcoholic drinks other than beer, and the "beers" may
have been large bottles as opposed to the usual contents of a
normal-sized can, bottle, or glass.
"I only had a couple of beers" seems to me to be completely true, though misleading.
However many dictionaries define half-truth as only partly true. And I really don't want create a philosophical debate about what is truth (eg., lying by omission), let's just leave it at that, that some people use this term, however much of a misnomer "half-truth" may seem to be.