Accepted answer
Start from what the certificate claims to measure and what the claimed measurement actually answers, because those are two different questions.
Comparison across certificates from different laboratories is almost never valid, even when the material is the same, because the methods are almost never the same.
The laboratory name and accreditation status can be checked in real time against the testing service's own register, and that two-minute check catches substituted certificates.
Industry guidance on this topic is consistent because it comes from first principles rather than convention.
Be careful not to over-read this — a certificate that is imperfect is not worthless, it is just a starting point for thought rather than an endpoint.
My working rule is that a document without a lot number, a method section and a test date is marketing.