I guess I've gotta be disagreeable. Firestone RH-5° rims can be killers at any location on the truck. They are dangerous to the guy doing the tire installation and mounting, and they can cause a wreck if one blows while driving the truck. I agree that the outer rears are most at risk of letting go and doing external damage, but they will do severe internal damage to a truck too if one blows at the other locations. To me there is no such thing as having them "in good shape".
The term "Budd wheel" is miss used. Budd style wheels, as crenwelge says, are stud piloted. Budd is one company that made that style wheels. They were also made by Kelsey Hayes and Accuride (nee Firestone). Motor Wheel Corporation made most wheels for Chevy and GMC and were hub piloted, but MWC also made stud piloted wheels for the other car/truck manufacturers.
All the wheel manufacturers got their outer rims from either Firestone or Goodyear. The Firestone Steel Products Company made the RH-5° outer rims. They were first introduced in the late 1940s and were a dominant component up into the 1970s. The last record I have of them is a 1976 Kelsey Hayes catalog listing.
Because of the danger of these wheels, no reputable tire shop will touch them for insurance and lawyer reasons. Stu