The AAIB report says nothing useful about it but Graham Hill's plane appears to have at some stage become de-registered from the US register but never placed onto a new one.
In effect, his plane didn't exist.
Since he was hardly short of money it was presumably a c0ckup by somebody who he trusted to get the papers right.
One way to achieve this nasty situation is to apply to the FAA for an Export CofA, as one would if transferring the plane to a different register, but for whatever reason
not proceed with the transfer. The FAA will then (usually if not always,
AFAIK) de-register the plane, without necessarily any correspondence. This could happen in a situation where you are selling the N-reg plane to a foreign seller who wants his local register on it, but he pulls out at the last minute.
Such a situation can arise with any aircraft registry which operates non-expiring CofAs (e.g. FAA, EASA, etc.) whose validity hangs purely on a Release to Service by an authorised person/company.
In GH's case, the company doing the subsequent maintenance would have had no reason to become aware of the de-registration. It would have been only had he applied for a field approval for some mod that the FAA may have refused the inbound 337....
It is believed that GH's insurer didn't pay out because the lack of registration made the CofA invalid, so the flight was illegal before it got off the ground. There may have been other reasons also but this one would have been enough.