What's this? For once we agree on something? Nah.
Propane does indeed burn cleaner in the real world as it gets closer to complete combustion than gasoline does. Here's the equation for complete combustion of propane with air:
(C3H8)+ 5(O2+3.76 N2)--> 3(CO2)+ 4(H2O)+ 18.8(N2)
You can see the only byproducts of combustion given complete combustion of propane are carbon dioxide, water, and nitrogen. The exact same byproducts, but in different quantities, result from the complete combustion of octane:
(C8H18)+ 12.5(O2+3.76N2)--> 8(CO2)+ 9(H2O)+ 47(N2)
Unfortunately all the stabilizers, additives, etc. they add to gasoline make it a lot "dirtier" fuel to burn. Gasoline isn't pure octane either. The exact chemical composition of gasoline is tough to track down as the seasonal changes made to aid in vaporization effect the composition of the fuel. Neither propane nor gasoline completely combust, but propane gets closer to it so it doesn indeed burn cleaner than gasoline.
90% combustion of gasoline will yield more carbon monoxide and unburned hydrocarbons than 95% combustion of propane will. More of the propane is burnt, so it burns cleaner.