Of course! I wouldn't think twice about it... I should be watching my child better if he did break something, so I obviously have great culpability
I was once holding my child's hand and he tripped over a skirt on a display table that was in a small area in the front of the store. I could not have been watching him more. A snow-globe came crashing down on him and he was cut by it.
I know my post will be picked apart by people trying to find fault with my parenting, so let me point out it was several years ago and I don't remember all the details, just that it happened really fast and I could not have been watching him anymore.
No, I did not offer to pay. I did not threaten to sue either. I took the band-aid they offered me and left the store to take care of my son.
Had he been running around and knocked into it and broke the globe, I would have offered to pay even if he was hurt.
So my answer to the OP, is --it would depend on the situation.