3 or 4 times lately, on my morning commute, I've seen a tall, pretty gal on a pale yellow "cruiser" bike. She has a great big messenger bag slung over her shoulder, and she goes pretty slow. Oh - and she has some SWEEET boots!
This morning, she was wearing a thick knit cap and mittens, a coat, etc. (Wow! If she's already cold when it's in the mid-50s, she won't do well over the winter.)
Perched on top of her stocking cap was her helmet. She must've loosened the straps, so it would sit a couple inches higher than normal.
The problem is - the only job that helmet is doing is keeping her cap from flying off. (If she were going 25mph faster, that could happen...)
I s'pose if she was using the top of her head for a battering ram, it might help. But in any realistic crash scenario, it's more likely the front of your head, or the back of your head, or perhaps the side of your head, that's going to need some cushioning protection. Every bit of bike-helmet advice I've ever heard says - SNUG helmet, riding low on the forehead.
A week or so ago I saw a little guy riding on the front of his dad's bike. He had a helmet on - but it was on backwards! With the pointy part in the front! (It looked very stylish, and appeared to be keeping the sun out of his eyes.)
(I wear a balaclava under my helmet on cold winter days, but it's made of thin material and has negligible impact on where the helmet rides on my head.)