The official policy is to not issue the visas the border... but in recent months (years?) this has been totally ignored.
Visas are possible and easy to obtain at border crossings for Americans, Canadians, and, well... most nationalities. Sometimes, because you're an American, they may make you wait for a few hours to piss you off - but they will grant you a visa.
I know this because I've been in and out of Syria three times in the past month and a half, each time collecting a fresh visa at the border. I've met half a dozen Canadians and about as many Americans who have had done the same. (Just don't go to Israel first... or SAY you're going to Israel after!)