Sure he didn't mean the M-14?
M-14 is no more reliable than the M-16 these days, but early on the M16 had a well-earned bad reputation.
Mini-14 was not around during the Vietnam war, however they were and most still are decidedly less accurate, more fragile, and no more reliable than the M-16. They certainly can't take the full-auto fire for long either.
There WERE actually alternatives to the M16 that were real and tested. The Stoner 63 was an excellent example. The Marines wanted the gun, but cited the advanced state of production/adoption of the M16 by the other services and roughly equal performance in the field as reasons for sticking with the M16. (This was pre-production Stoner 63's vs. mature production model M16's, but I'm not second-guessing the Corps on this decision. It was sound.)
The AR-18 was also under-developed and unappreciated although many aspects of this Armalite gun were doubtless superior.
In the end, the M16 had the momentum, ergonomics, sex appeal, and it was just Good Enough to preclude the use of any other weapon.
BTW, I'd have preferred the M16 myself were I over there... Then again, I know how to clean the gun too. If you'd given me a Mini-14, i'd have tossed it for anything else the first chance I got. I'm talking M2 carbines, Grease Guns, Tommy guns, BAR's, M60's, Sterlings, Stens, MP40's. Whatever, so long as it fired quick and reliably.
The BS artist you got the gun from might have been an armorer to keep him out of the field!!!