Reading a certificate means checking four things before anything else: traceability to your vial, the test date, the analytical method, and the identity of the testing laboratory.
Batch versus lot is a semantic distinction that determines whether one certificate applies to ten vials or to one, and checking this distinction is worth a minute.
The field you have least reason to trust is the one that looks most impressive, because appearance and accuracy are not correlated.
Pharmacopoeial standards require method validation steps that research-grade certificates almost never claim to meet, and the absence of that claim is itself information.
The limitation is cost — truly rigorous testing on every lot is expensive enough that most people do not do it, which is exactly why the variation matters.
If the certificate does not trace to your vial, it is not evidence about your vial.