Would a country/army be able to frame the US for nuking another country (i.e. China)?

the fallout material is typically unique to the source of the bomb. Plutonium or Uranium, which isotope, how thoroughly has the reaction depleted the fuel. Was the device efficient or dirty. Scientists CAN determine the source of a bomb by its fallout materal, if they're given a chance to do so, but if an agenda like that was underway, all the airwaves would be on lockdown donchya think?