Ah ha, yes, I do see where your coming from now. I'm afraid I can't speak for America because I am slightly ashamed to say that I don't know the place, and have never been there, so you have the advantage I guess.
However:
When the client came to me and said "I left my drive here" that's his truth."
Yes, I agree with that, that being his knowledge of events.
My truth was "our systems tell us the drive was picked up".
Yep, your systems do indeed tell you that.
"Where is the evidence that he didn't?"
There IS none, other than his word.
Can I prove beyond a reasonable doubt that he did?"
Well, ideally, you should be able to fall back on your systems, after all,
"I have lots of systems in place to prevent that".
However, as you feel that you cannot use what your systems tell you as evidence, perhaps your systems are not very efficient or fit for purpose? Otherwise you would have used them? After all,
It turns out that they hadn't failed"
, well... actually they had?
Can he prove the opposite?
No, he indeed can't prove that he didn't.
Just wondering, might it not be a good idea to have some kind of ticksheet system in place, signed by the client, so that in the event of a possible dispute... well, actually, there wouldn't be one in that case... or would there?
I am also wondering what the point is in having "lots of systems in place to prevent that", if you will never be able to rely on them in the first place? Seems like a waste of time?
Another small matter (although less important, why didn't you just give the client a replacement for free, instead of writing a cheque? Or didn't you have that item in stock at the time? Or wasn't the item bought from you in the first place?
Problem number 2 is that I will lose their trust, their business and the business of many of their associates and friends. By honouring the man and his truth, I will have many more opportunities to make far more than a mere $120.
Although you might consider it a small risk, your making an assumption that your going to get the business of his associates and friends. After all, they have their own mind and can decide where they want to do. In your mind, it is a hope and NOT necessarily a guarantee.