Maybe it is just because my dad was super strict, or maybe it is because I know what one of those sheds cost and how much it costs to have a new door sent out, but I totally can see them reporting the theft. But, I have always thought that the fact that the gas cans were the only thing missing, they had to have known it was her. This was, of course, before finding out she actually broke the shed. My father would have reported it if he thought that it was me to teach me a lesson.
ETA: My dad would have given me the gas if I asked, but if I broke his shed and stole it, he would have reported it.