Wow! I've never heard of Cartier returning unauthentic items "all smashed up". That's actually illegal. Cartier would then be responsible for the replacement value and, unless they can prove that the item wasn't authentic -- without a doubt -- they would then have to replace the item with what the customer claimed to have sent for repair.
I do agree that Cartier won't accept items that have been altered by a jeweler other than those authorized/employed by Cartier. They will, however, bill you for the time they spent determining that the item had been altered and that there is no note of it in their service records.
Again, I would only purchase from a Cartier boutique, an authorized Cartier dealer, or someone who you know for a fact sells only authentic pieces.
This is a great idea! I would definitely try this! The only problem I could see is if the original purchaser's name is in their computer and your details don't match... but then the piece would have had to have been purchased fairly recently. Otherwise, I don't see a problem in requesting that a new certificate be issued for your item. The fee would be worth having documentation!