The only way a DB would be applicable here would be as quick way to call up previously scanned images.
In contrast, the CoLB is indeed just a database printout that has been certified to be correct. At some point, the DoH computerized their records. They went through all their paper and entered key facts from each document into a database. Now, when somebody asks for their birth certificate, they just key the person's info into a computer application which looks up the database record. If the data looks right, they click a button, and the program prints the key facts out on safety paper. They take the paper off the printer, stamp it with Dr. Onaka's signature stamp, emboss it with the state seal, and send it out to the citizen and cash his check. No more dusty files or photocopy hassles (except for the special cases, like this one).
That would be one way to DB it. The other would be to attach image files to records in the DB.
This looks to me to be an image file (paper curl again.) If it were found out that image files aren't used - they use the method you describe above - then something would be amiss. Or, as you say, a special case here where they went and scanned the book.
Also, I count 8 scans needed along with the field data. Another reason a document scan, DB and image server makes more sense - assuming they are paperless in some form. They could be old style and pull the book, make a copy...