Not so.
Close enough.
There are headspace differences between the two rounds. The .308 go-gauge is 1.6300, the .308 no go-gauge is 1.6340. The 7.62 go-gauge is 1.6350, the 7.62 no go-gauge is 1.6405. Since NATO military ammunition can come from any NATO country, and the goal is the ability to interchange ammunition, the military chamber is larger.
Provided we use common sense, headspace differences shouldnt cause us to quake in fear. If a person is using new, Mil-Surp ammunition; and not reloading it, then the headspace becomes a non-issue. The round is fired and expended.
http://www.surplusrifle.com/shooting2006/308vs762nato/index.asp
Close enough.