Factory checkup just before selling...

I would think the factory could verify. I think on some items it is worth doing, on others not so much. I bought a small Audience Power Conditioner that had a factory check, cost the seller very little to do, and made a difference to me as buyer...

I’ll usually buy anything, but those ads put me off. I would rather have no story than half of one, YMMV.

Suspicious but simple to verify 

Ask for paperwork and or call the manufacturer- these are generally very small firms and recent service will be remembered.....
i am currently sending a rare phono preamp across the pond so it’s creator can not only repair it but give it a clean bill of health before I sell it....
not needed on everything for sure...

I bought a preamp at a good price the owner clearly stated it had been sent for repair after being damaged in transit to him when he bought it secondhand... , and he added an upgrade, which took so long from the original manufacturer... he bought a different preamp in the meantime. SO I got a good deal in my opinion.                  
I really think no one is going to send in a fully functional device (Unless they wonder why does it not sound very good? and discover well that is all it ever will be) I could see sending it in for a checkup to be sure it is not damaged, since it just does not sound 'right'. But personally I think that scenario would be pretty rare, and the sent for repair is the real typical thing.