OK , so you make your phone call and give the information necessary to fill in a COLB form (even though it isn’t going onto that paper form directly) and that creates a (computerized? which in 196x would mean a punched card) data record from which a paper COLB can be generated upon request ,, not the paper COLB itself; not much of a distinction.
Not at all. You'd have to fill out the original form, just as a Certification of Live Birth is filled out. A home birth still goes on the Certificate oLB, as does a delayed birth. A Certificate of Hawaiian Birth is a different form. But in '61 those would have been "stored" on Microfilm or MicroFich. It would take several punch cards to hold the information that is on the abtract. (remembering that the standard punch card was 80 characters.
WND had a good article detailing the ways to get such a "source document" in 1961.
Keep in mind that the information on the COLB had not been verified. Just the birth location listed on the source document, which may, or may not, have been fraudulently filed.