>Sure, but with sufficiently many people, these effects will usually average out.

No they won't. If you have two correlated factors and only measure one of them you can easily get to totally wrong conclusions.

If you have a food that is more often eaten by people doing a lot of sports, you will measure that eating that food is correlated with being more healthy. But it would obviously be fallacious to conclude that this food is more beneficial to health than other foods.