It would make sense if it were a 1965 rifle to not have a serial number. Serial number requirements didn't happen until 1968 like he said. I wouldn't sweat it. My son has a shotgun with no serial number. It's very old. It makes it extra cool if you ask me. Legal and no number from the man on it!
"Always place your clothes and weapons where you can find them in the dark"
"Understand that the enemy is not the enemy in his own eyes ;this may offer you an opportunity to make him your friend. If not, you can kill him without hate, and quickly."