I understand you are getting your info from a web page,but that web page is wrong. It must be a typo. The US military were still using the old 30/06 Brownings as their medium machine guns all during the Korean War,and didn't even adopt the 7.62x51 Nato round or the M-14 until around 1954.
It's a typo. In any case, I doubt that this fallen SEAL has a '60 anyway: It's been removed from service.
If this SEAL had a 7.62 NATO belt-fed LMG, it was an FN-MAG -- the US military calls it the M240.
The FN-MAG is the LMG that we should have been using all along since the late 50s anyway.