I was a California notary; I did not require that I witness the signature for an Acknowledgment.
An acknowledgment says only, "John Doe, whose signature is on this document, came to me, demonstrated to my satisfaction that he is John Doe, and swore to me that he signed the document."
I do require that I witness the signature of a Jurat - a Jurat says, "John Doe came to me, demonstrated to my satisfaction that he is John Doe, and swore to me that the things stated in this document are true, then signed the document."
One of the recent changes in notarizations that permission letters are more frequently notarized - they require that somebody personally appear in front of the notary, with sufficient identification, to mitigate the possibility that a signature is forged or coerced.