Nothing wrong with due diligence and eBay have a system that we have found works well for this scenario (can't say about other market places).
If we have a customer claiming DNR but the tracking says otherwise we say take the normal steps, make sure noone else has picked it up and put it somewhere in the house, Check the place the mailman/delivery people normally leave parcels then if no luck open a case with eBay. (basically what
@kulture suggests)
Just this is enough to put someone that is lying off.....psychological barrier....we don't hear anymore of it.
If the customer does open a case eBay will ask us for details, we put the tracking number, which presumably eBay check because either we don't hear any more about the case (but don't get struck by eBay either) or in the rare case the customer does give eBay details, eBay will order us to send a replacement which we will of course do.
The last out come is rare. If a customer is lying just getting them to make a story up...fill in any form or details....more often than not you won't hear from them again.
It might be unethical, it might even be pushing the law......but send your customer on a guilt trip and that normally flushes out if they are talking BS or truth.