The issue here is airspace management and deconfliction; you can’t conduct air operations with a third party noncooperatively flying in your airspace without putting aircraft from both sides at extreme risk. This is why we don’t permit non-allied forces to operate in our AO in Afghanistan or Iraq. Putin could have asked us to be allies in this operation, but Obama clearly sides with the radical muzzies over Assad, so that is a no go. He could operate with us in his airspace, which eventually will lead to someone losing aircraft and could spark WWIII; probably not a good idea. Or he could tell us to stay our of his AO; most sensible choice given the options. What else is he supposed to do?
Your post is logical and based on fact. The nations in that region understand that the U.S. is all talk and no action, and that is because Obama is a pussy.
Putin on the other hand, means what he says, and they know it.