Yes, of course.
What I meant was, how can we establish that they were IN FACT the officials in those positions?
No problem. Surely the Brits have records who who held what offices, even “chief clerical officer” type positions, in the colonies.
But that doesn’t help, really. A good forger would have already found out who was the principal registrar for that place at that time and made sure he used the right names.
I think authenticity would depend more on forensics— examining the paper, ink etc. In the end, it may be impossible to be sure one way or the other—modern documents are mundane, nondescript and exist in monstrously huge numbers.
Unless, of course, the forger slipped up and didn’t do his research right.
But it’s the Obama side in whose interest it is to show that it’s a fake. Authentication really is saying, “well, at least we can see no obvious signs of forgery.” A perfect forgery, by definition, would never get detected. Of course, absolutely perfect forging is extremely difficult, so an authentication that says, “no apparent signs of having been forged” is, for practical purposes, accepted as proof of not being forged.