I presume the postie in question rung in ASAP about it.
If that's the case, I'd be asking why the spare wasn't brought out to them. In my unit keys have been issues in the past, and usually the spares are taken out within 30 to 40 mins. The 4 hour delay cannot be blamed entirely on the postie as long as the manager was informed. They may be able to argue against paying for that type of delay, but waiting 4 hours for, I presume, the RAC to turn up and recover the van, that's wrong. They didn't cause that delay, so are not responsible for it.
As for fact finding, a bit harsh, but would say they can do it. But, it was an accident, we all make mistakes. Think the boss is being a twat, and trying to impress someone above, also starting a trail of paperwork which may well be used at a later date.
I would personally say that a quiet chat and maybe a counselling are as far as it should go, if that far at all.
They may try something based on security rules, failing to safeguard property or some such crap.