Surely, as the record has been opened in contravention of the DPA, the onus is on the companies to provide proof that this is appropriate -- ie proof of death --rather than on me to try to provide proof of life?! Never mind the fact that seeing a copy of a passport doesn't prove that anyone is alive!
Although it isn't clear from what you are saying, it is possible there is an element of them wanting to verify you have the authority to request re-closure of the record.
The law on data protection isn't just about the publication of information, but also covers the appropriate handling and processing of it. Rights in connection with personal data are held by the individual, not the public at large.
Therefore it could be a breach of the legislation for an organisation to 'process' an individual's personal data on the say-so of a third-party. The onus should be on the requester to verify that they have the right to make the request.
I'm with BumbleB in terms of being happy if it were my record inadvertently opened. I would be
very unhappy to discover a meddling third party had taken it upon themselves to have
my record closed without my consent.
So, even if they aren't consciously doing it, I think FindMyPast should really be seeking some evidence that a request for re-closure is being made by or with the consent of the subject. A copy of the passport or driving licence might be a reasonable proxy for consent as they aren't documents someone unconnected to the subject would normally have access to.