[markeb01]

The main reason for running tubes on the original rims isn't so much to make sure the tires will hold air, it's because the original rims didn't have safety beads formed into the rims. Safety bead rims were pioneered by Chrysler in the mid 50's, but didn't become standard equipment with the other manufacturers for another decade or more. In the days before enlightenment GM and Ford provided tubeless tires on non-safety bead wheels as standard equipment for years. Now it's a liability issue, like the tread belt/tire failures with Firestone a few years back. The benefit of the safety bead was the tire wouldn't separate from the rim if it went flat, or peel off the rim in a hard turn with an under inflated tire. For us do-it-yourselfers the advent of the safety bead was a pita, making it much more difficult to mount and dismount tires with hand tools.

Even the older 50's-60's rims that were held together with rivets will not leak with tubeless tires, unless something is rusty or defective. With all that said, it is a good idea to run radial tubes in radial tires on these old rims as extra insurance keeping everything together in case of an under inflated tire or a flat.