Seems to me M1A rifles in .308/7.62 are easily found/bought/owned/shot. I've shot more than my share of them and am currently searching for one myself.
Quick search of the wiki-machine reveals and entire page for this rifle and it's M14 military counterpart.
Are you trying to catch him on a technicality here? I mean seriously, lots of people toss that '1' on the end. it's harmless. I can walk into H&H and ask for an M1A1 and they'd take me to an M1A.
I think most readers hear know he's not referring to an Abrams tank. (FWIW: there was an M1A1 version of the M1A rifle that was a carbine length folding stock version. pretty cool looking!)
Well, you edited your post after i responded. Or during my response. Either way there is apparently a lot of confusion between an M1a...
which shoots this...
and an M1a1...
Which shoots...
although my faith if H and H is not 100%, I dont think they would confuse the two.