I keep it in the cupboard, I should think it would crystallise in the fridge?
Some medications are meant to be kept in the fridge but the instructions always tell you this. Over the counter stuff isn't usually needed to be refrigerated, it's certain antibiotics and I think insulin etc.
I guess maybe people do this because it's cooler if giving for teething? Or maybe it's the safest place the kids can't reach in their house? Maybe it's just because some people prefer to put stuff in the fridge if they're unsure.