Most parasites humans contract come from eating pork, beef, game meat, animal organs, freshwater fish, milk, contaminated soil, pet feces, and sometimes fresh produce (and fruit juices). Pork tapeworms literally hatch in your stomach and can grow to be 10 meters long, feeding off the nutrients you eat.
With the exception of pork, this line is mostly bullcrap. Reasonable hygiene is all that is needed. I eat mostly wild game, game birds, game fish, often hunted and processed by me... or locally butchered beef, chicken, and turkey, often raised, butchered, cut, and wrapped by my own hand.
Cook your dang food to medium and any parasite or parasite eggs will be dead. And that goes for ANY meat, not just wild game and farm raised. Your most likely avenue toward parasites or bugs is due to poor handling of birds and pork particularly, and eating meat that is rare. 99.9% of the risk is gone simply by proper cleaning and cooking... The rest is probably through poor preservation practices, though your belly and nose generally won't let you eat that anyway.
PS: If the dog won't eat it, you'd better not either. But that only works in the negative... If the dog WILL eat it doesn't mean you should (he'll eat cat poop, for Pete's sake).
All this scary nonsense is just that - Nonsense.