Hmm, I don't recall the manual mentioning that either! You'd think they would mention something as common as that. When we tighten the straps up, they compress the coat quite a bit, though it is hard to get them tight enough with the coat on.
I'm not exactly sure how it would be generally feasible not to wear a coat. I mean, the poor kid would freeze to death in the 5 degree weather every morning, even if we put a blanket or something over him. And there's no way for us to warm our car up beforehand.