Indeed provisions vary. From my Amex the terms state
Originally Posted by Amex
Claims for lost or delayed luggage must be reported to the transport provider or carrier and a property irregularity report (such as a luggage incident report) obtained where reasonably possible. If a property irregularity report or incident report is not provided,
You must provide evidence that You have taken reasonable steps
to obtain a report, such as emails, call logs or other reasonable evidence. A copy of any property irregularity report obtained from the airline must be supplied to Us together with the following information:
a. full details of the flight (airline, flight numbers, departure airport, destination, scheduled flight times and arrival airport);
b. details of the delay or loss incurred; and
c. full details of expenses for which reimbursement is claimed.