There is a TV series called "Graveyard Carz" and the shop that is the subject of the series is dedicated to the restoration of MoPar carz. They detail the restoration to the Nth degree. For example they will put a dab of paint on the trans or the rear axel where one would have been placed when the car was manufactured. These are witness marks if you will (my term). These marks tell the next assembler that the job prior to his or hers was DONE. They also would tell an inspector that the job was done. The color of the dab might also tell the person what ratio rear end was put in or what transmission was put in and this should agree with the order for the car. Back in the sixties the cars were painted by humans, and not yet by robots, so that the underbody would get overspray on it, but the car was not painted underneath. Certain areas were "undercoated", such as the wheel wells, but not the entire underside of the car.
As for muscle cars all being built with frames or chassies, this is not the case. The Barracuda was unit body as was the Chevy Nova SS, and the Camero, and the Mustang, as well as the AMX. The Chevell had a frame under it at least up to 1967. I have a 1967 Chevell SS 396 and a 68 Camero SS living next door to me. My 66 Mustang 2+2 was unit body as were my 68, 69, and 70 AMXs. I fairly certain my 69 Dodge Charger was unit body. E-gad I wish I had kept some of these cars. I had a 64 Studabaker Avanti that was fiberglass body and a full frame, like the Corvettes. That was supercharged with a paxton blower. That was a great car. IIRC the other term for "unit body" is monocoque - (spelling) pronounced mono-***. European manufacturers were doing this for decades before the U.S. auto makers.
Many "muscle-car" folks will detail the underside of the car and paint it as a way of detering corrosion and give it a more complete appearance. Most "muscle -car" restorations are not being done for "concourse de elegance" competition so that variation from "original factory finish" is generally acceptable.