The M16A1 was not adopted until 1967.

Various "off the shelf" AR-15s were purchased by the government as well as small batch contracts, most notably by the Air Force as an early adopter.

This picture is low res and JFK's hand covers the side of the receiver, but I am relatively confident that the flash hider in the photo is a prong type different than the XM16E1, making this either an AR-15 or a very early M16 (no suffix designators). While I can't definitively say what it is, an M16A1 it is not.

Yup