Have a look at their conditions of carriage
here. Article 15.4 sets out their liability for baggage (at SDR 1131 per passenger) but certainly does not state a requirement for receipts to justify any claim.
This is your contract with them and if they wish to limit liability (by requiring receipts, which is a questionable requirement because very few people do this) they should, at least, set out their requirements in their contract.
I would reply stating that there requirement is not set out in their CoC and therefore is not valid. You might want to find local ads for the same/similar bag showing that your claim is a valid one and will allow you to replace the bag that they damaged.
If this doesn't work you might want to get in touch with the
AUC, who have been known to intervene.