I decided with all the confusion about this that I would take a picture of mine with a .32 S&W Long round and a .32 ACP (I don't have or load .32 S&W shorts, but the length is roughly the same) in the cylinder, then I realized I didn't have any .32 S&W L., so I had to load some.
Anyway, you can see that there is a TON of space for the .32 ACP to jump until it reaches the throat, while the .32 S&W Long looks *gasp* almost perfect, as if it was meant to be shot in this gun.
It's not like this is the first time a revolver manufacturer failed to be more specific with the cartridge the revolver was chambered for, Charter Arms back in the 70s/80s had the 6 shot .32 Undercoverette and they never specified on the barrel whether it was .32 S&W, S&W Long, .32 ACP, or even if it was .32 Colt.
At the time .32 Colt was basically dead and obsolete, but they expected people to realize that if something didn't seem right they wouldn't shoot it.
When the cartridge is on the barrel and the cylinder closes and functions with .32 S&W Long in it, I can't think of a reason it's not the "right" ammo to be used.
The 5 shot H&R's with the shorter cylinders, I'll bet you can't even close them with a .32 S&W Long loaded in them.