No, the parasite that causes trichinosis is found not just in domesticated pigs but in many wild animals. Obviously paleo man wouldn't have been eating domesticated pork but I guess he could have gotten it from wild game, though I have no idea if it was around in the paleolithic. If so I doubt paleo man "avoided it"; before modern medicine and sanitation, infectious disease was (and still is in some places) a leading cause of death. Having said that the majority of trichinosis cases aren't fatal or even severely symptomatic. Probably they had food customs/taboos involving not feeding certain foods to children, pregnant women, and other vulnerable people after noticing their potential to cause disease. That's found in pretty much all cultures, I think.
Edit: It's true that today one of the causes is feeding raw meat to pigs (including rats, yeah) and not all species of the worm cause disease in humans, so I don't think trichinosis would have been a concern for paleo man.