Maybe the 1964 signature date was when the records were updated after the 1963 law was put in place? It definitely does say it was first recorded in 1961.
Most have suggested that the 1964 date corresponds to the time of the O sr divorce. They had to send off to get a record of the birth. Therefor the 64 date stamp.
This does follow the time line of the divorce, which makes it partially pass the smell test. I find the most interesting observation is that the folds on the paper exactly correspond to the folds on other BC’s, all of which were stuffed into little yellow envelops.