Y'all need to differentiate which rims you're talking about, two piece or three piece.
The two piece has a locking ring that fits over the rim and slides into place. The major problem with them is due to rust. If the rim is in good shape it is a reasonably safe rim. These rims are not the ones that usually cause problems.
The three piece rim is the one known as the widow-maker. Again, corrosion is a culprit due to the way everything must be properly seated. Problems with these rims were few until the 60's and 70's when inexperienced people started working with them. The older guys knew how to handle them properly, what signs to look for during assembly and where not to stand during inflation.
I'll pay the guy at the tire store the five bucks to dismount or mount the tires on the lock-ring rims. For a couple more bucks they'll get rid of the old tires, too. You can dismount them yourself, but I can't see working that hard for five bucks. If you have the three piece rims, they're even harder to get apart, and unless you in a restoration of a big truck where there are no substitutes, get rid of them.
