While the 7.62 chambe is 'loose' compare to the 308WIN chamber... the thing one would really need to worry about is the pressure.
.308 Winchester
Maximum: 62,000 psi
Maximum Proof Pressure: 89,000 psi
7.62 x 51mm NATO
Maximum: 50,000 psi
Proof pressure: 67,500 psi
Any well constructed rifle does not fail outright due to pressure problems. It'll take time and other factors to be involve before it fails. The most notable would be a weak action (ie Mauser), which I don't feel is the case for a M1A/Garand action. If a rifle is well taken care of and not 'used and abused', IMHO... it'll take 308win rounds without issue, since most commerical ammo are never loaded to full SAMMI spec. BUT if that's all you planning on shooting, maybe a swap to a commerical 308win barrel would be more insurance for yourself.
The only KB that I read into is the report by Dr. Bruchey funded by FA. And the failure was actually from bad treatment of the barrel resulting in more than usual stress factures around the chamber which resulted in the KB.
My barrel is marked 7.62mm and not .308win, but I generally shoot mil-surplus through my M1A... just because it's cheaper than anything else out there. But every once in a while I would dump a box or two of commerical through it just to use it up.
When it comes down to it... how safe do you feel?
~nb