I would think that producing a believable forgery would be very hard. For instance, typewriters have “fingerprints”. How would they be able to duplicate the typewriter fingerprint from the typewriter used to produce birth certificates from the same week or month. Also, aren't these birth certificates numbered and tracked on various ledgers? The forgeries would need to account for these ledgers as well.
After almost 3 years, if it were possible to produce a forgery, it would have been released by now.