Impurity Of Saliva Of Stray Animals
The advice of the prophet (PBUH) is for stray animals which might have filthy mouth. It is not that their saliva itself is a thing of filth like their urine. The Quran mentions that the hunted prey of the trained beast of prey like dogs, is halal and pure, which does have some saliva of theirs in it, when they catch the prey in their mouth.