Andy and the Gentleman Crook - S1-E21
Visible crew/equipment: When Aunt Bee is in the kitchen preparing to take a tray of food to the prisoner she momentarily walks out of the kitchen through the swinging door. As she pushes the door open, a crew member's hand and arm can be seen behind the door.
Answer: It was a joke. They were supposed to be dumb hillbillies.
Both. According to later interviews with both Andy and the Dillards band (the real name of the band that played the parts of the Darling children, of which Charlene (Maggie Peterson - Mancuso was also a member) the reason the Darling boys never had any lines was because they would've had to have been paid if they spoke. In return for appearing without lines or pay, Andy promised to get as much of their music onto the show as possible which, he did. This obviously gave them a lot of exposure.