then it would have happened more uniformly and not only on a few fields
also, we should be able to find the exact same thing happening to other birth certificates from the same scanning batch (year/book)
would be trivial to prove, if its real...
of course, we not allowed to see the other birth certificates from that day...
Not necessarily. The algorithm would have to recognize it as text or something else appropriate for the b&w layer. Anything on the original that was faint enough to be read as background image wouldn't be converted. That's why some of the numbers are black and some gray. (You'd have to ask why, if someone was forging this, they'd use a combination of pure black and grayscale numbers. Why not use the same numeral '1' each time?)
also, we should be able to find the exact same thing happening to other birth certificates from the same scanning batch (year/book)
If someone else got a photocopy of their birth certificate (something they don't usually give out) and scanned it on the same type of scanner with the same settings, yes we should. I'm not sure how many of those there are, though.