over the years i have had a few things like this happen . couple of them were my fault so i either fixed or paid for it. i had a customer once that said someone switched is transmission case with one that was useless ,and at that time i had only 1 of those case in the shop so it was imposible but the customer being a bike shop that was doing lots of show bikes i didn t want word going around that i was switching parts with older ones .i told the shop i would pay for it as a good will but that it was imposible that it could have happened in my shop, so i paid for a new case plus i had to polish the new case ended up costing me 500 $ for a 100 $ job , sounds expensive but this is like 10 years ago and that shop still gives me business all year round .
what would have happened if i would have refused to pay ?
i would have lost that customer (10 years x $$$$ per year) + probably some other customers that would have heard his side of the story

i m not saying you have to take the blame but like Figurellc says
i suppose your actions would depend on how much you think his bad word could damage your rep
i don t like taking the blame for something i did not do but i have to look at it as a business decision .$$$
taking pictures of all parts is too complicated for me but i try to go over the parts when i receive them and take pictures only if i see some damage .
before you do some parts for 50% ofthe price remember that if something goes wrong you will pay 100% of the repair
being a mail order thing i would sure want the customer to send me clear pictures of the damage and also clear pictures of all sides of the package
or shipping box it was in .
sorry for the loooong post