I share your reluctance to give full credit to a President. GW Bush didn't cause the downturn, but people could probably point to actions that made it worse--most people agree the deregulation of finance caused harm, others would say monetary and tax policies that increased foreign capital in US markets increased speculation. 

Obama can take some credit for reducing foreclosures due to medical bills. I worry Trump will be given credit for inflation if he pursues growth at a time of full employment.