Well, first off, they cannot be kicked out because some people were annoyed by the shoes. And secondly, unless this was a high end restaurant that doesnt allow children, you should expect kids to be there, and at that age, kids can be loud.
So, yes, It was extremely rude, if it even happend at all. Because the more I think about it, the more I dont believe that story.
I still don't see how it was rude. Restaurants often will give freebies if they think something was annoying the customer.
Is it rude because they didn't reward the obnoxious family? Why would they? And yes, any owner of ANY business can kick someone out for that reason or any reason if they deem necessary. It was not high end, and there were more than one family with kids (us included) but no other family thought it was acceptable to let their kids wander around the restaurant, let alone with shoes that let out a loud squeak every time she stepped. And I wouldn't expect that at any place other than a McDonald's or a Chuck E. Cheese or some other place that is specifically for kids.
You can choose not to believe it, but it did happen. And unless there was any doubt, it was served to us with specific apologies.