Viability of reduction of oil paint binder and solvent flammability upon disposal via addition of water
It really depends exactly on what you're mixing the water with. Soaking a rag or paper towel will reduce the flammability and is recommended by many safety organizations online (here is one). However, if you are washing off a large amount of solvents or flammables with water and the chemicals are immiscible in water, it can sit on the top of the water and still burn if exposed to some ignition source.
The best thing to do is to look at SDS or MSDS sheets if you are unsure what the best disposal procedure is for some chemical you are using. Additionally, a google search should offer additional information on disposal and hazards of the substances painters used.