No, America is cleaning up Georgia's allegiances to fundies. Probably spurred by corruption, mafia, bribery by the Saudis who wanted to keep the region unstable. How do Chechen rebels get from Afstan to Chechnya? Iran - Azerbaijan - Georgia.
Putin knows, but it seems some of the Russian cold warriors and big mouths don't understand that this is a good move for them. What better than to take out Chechen rebels southern supply route? Russians couldn't do it.