Not the bolt handle, the bolt body. It appears to my eyes as a smooth round cylinder. The only controlled round feed actions around in that era were Mausers/Springfields/Arisaka/other milsurps and Winchester M70s with the distinctive "claw" extractor.
I don't think anyone came up with "Push CRF" until the WSM line of cartridges came out.
The bolt handle looks like it has a small divot in the bottom which is something I've seen on M70's, but the rest of the action looks like Rem700, from the safety to the bolt body. Which is funny because the Army didn't officially use M40s in Vietnam. But it could have been a unit purchase from the PX modified by an armorer or an M40 swiped from the USMC.
Jimro