With a crown there's always a risk that you could trigger root failure. You could end up with a different problem. You could ask them to replace the filling, but each time they drill a tooth and add a filling they have to use a bit of acid to make it all stick. If you broke the tooth it could be that it doesn't have a perfect structure for a crown. They may have had to fill below the gum line. You should really discuss your options with your dentist as they have all the information. Ideally go for a second opinion at another dentist. They should run through all the risks and the likely outcome.