Even if someone were willing to send us "strong" ID, we don't have any special knowledge of what official government-issued ID looks like in every country where we have customers, nor the human resources or automated technology to investigate in detail whether any ID that is sent might be faked. At best, we could find an image of a passport/driving licence/whatever from that person's country and see if what they've sent us looks about right and matches any personal details we do have for the data subject.
Our disturbing conclusion was that if someone did ever send us certain types of request in connection with certain accounts, there might be no action we could safely take to resolve the situation that would definitely be lawful. If we get scammed by fake ID then we're breaking the law. If we don't accept ID that is real and comply with the subject request, we're also breaking the law.
Fortunately the affected services aren't doing anything particularly exciting or risky with personal data either, so it seems unlikely that any serious harm would come to anyone whatever happened in our case. However, the same basic issue surely affects many other data controllers/processors, and they won't necessarily be such unlikely targets as the research here shows. I haven't yet found any practical guidance from the regulators on what would be considered reasonable in this sort of situation.