I am inferring from the information that you have provided so far that it is game over if the user loses the receipts?
Yep. Fortunately, you could also store an encrypted receipt on the blockchain using a custom operation. It would just end up being slightly more expensive to store them on-chain. It's not like there aren't cool solutions to that 'storing' problem. Not having that problem would be nicer though - of course.
Well, if you manage to secure the private keys for your accounts, you should be able to do so as well for receipts. You could easily store them next to the wallet of private keys in your browser (though that would require regular backups instead of just a single backup) - but I (and probably also Dan) agrees that the storage problem in the STEALTH solution is somewhat delicate.