3 solid arguments as to why the "only fluids spread the taint" is bollocks:
1. If bodily fluids truly did spread the taint, including the stuff from a Grey Warden, then that means Grey Wardens can never ever engage in a lethal fight with other people nearby, as a bodily fluid know as "blood" comes out of humans when you poke them too much with a pointy stick. Fights can get messy. If a non-Grey Warden fights alongside a Grey Warden, there's a massive risk that they'll be wounded and blood from the GW will get into the wounds of the non-GW.
2. If touch could not spread the taint, including for darkspawn, that would mean sentient darkspawn can co-exist with non-darkspawn creatures. They cannot, that is why the Messenger and other sentient, talking darkspawn are such a moral dilemma: they mean no harm, but anything they do causes harm to non-darkspawn.
3. It's just not true, period. The lore/codex entries in the games themselves quite literally contradict the 'taint is spread via fluids' theory.