Strictly speaking it's not raw meat that makes people sick. We regularly eat raw fish and oysters, sometimes eat uncooked beef, and once in a while even chicken tartare. It only makes you sick if it has become contaminated with the dirtier parts of the animal or has begun to decay (or the animal is inherently "unclean" such as pork).

In European history the precursor to the germ theory was the miasma theory of disease which held that foul air was the cause of sickness. This actually fits quite well with the experience that people who live in the [smelly swampy parts of town get sick quicker] (http://penelope.uchicago.edu/Thayer/L/Roman/Texts/Vitruvius/1*.html#4.1), and that the meat that smells bad is probably not good for you.

Functionally, the miasma theory worked well. It led to improvements in sanitation as a byproduct of better handling of waste and improved sewer gas venting.

In contrast the germ theory requires that we believe in invisible tiny biting animals.