It depends on whether or not you are determined to teach your children to be responsible adults. I wanted my kids to be responsibile adults so I paid when they broke something and I made it a teaching moment.
If my kids knocked over a display of cans in a grocery store (pushing a grocery cart and couldn't see where they were going) they and I picked up the cans even if the grocery store said, "Don't worry about it. We'll take care of it."
If my kids opened a box they weren't supposed to, I paid for it and made it a teaching moment.
If my kids went to a neighbor's home and broke a lamp, my kids paid for it and I made it a teaching moment.
I paid for lots of stuff they broke that I probably didn't have to. BUT today my kids are good, upstanding, honest responsible adults teaching their kids to be just like their moms and dads. I'm proud of them.
Earlier today some mom wrote that she had had it with her 21 year old son. He wouldn't work, wouldn't help around the house, etc. She was asking about throwing him out of the house. The time to teach her son would have been at 21 months, not 21 years. YES, I'll pay for the lamp because I wouldn't want any of my children to be still at home and me wondering if I should throw them out because of their lack of responsibility and respect for the property of others.
And for the lady's supposed comment, "has just been determined to break something of hers for some time now ". Any one here had a hard day with a three year old and may have said something you may not have really meant at the end of "one of those days"? I sure have.
Try walking a mile in her shoes. Be a little understanding and a little more forgiving.
Good luck to you and yours.