At those temperatures, the H2O is the "dirt" in the mud. The liquid is probably methane.
What sort of temps have they measured?
I believe that at Titan's temperature, the only "flowing" going on is liquid methane. I also read somewhere that Saturn's huge mass exerts an enormous gravitational pull on it's moons, so perhaps the flowing rivers are due to the pressures on the methane which causes it to ebb and flow like earthly tides do.