My theory is that this confusion began with the 308 CETME, which had dimensions similar to NATO 7.62x51 but was loaded quite a bit lighter. Many small ring Spanish mausers were chambered for that round and the early CETMEs used it exclusively. Later versions were designed for the NATO round, and of course recent military arms are generally overbuilt for reliability.
I am sure that many of those old mausers have been fed a steady diet of 308 win or 7.62x51 NATO, but the fact that they don't fail catastrophically doesn't mean it is a wise practice.
I don't think the Enfields were ever designed for the CETME round, so the margin of safety should not be so slim.