Actually, I think there may be a third way. Today, the Saturn I won in an auction came in. The guy who sold it to me said it worked with backups, but he said he didn't know if it was modded or not. So I figured it was since he didn't use the swaptrick to play his backups.
Well, I unpacked it, hooked it up and tried an original game which worked fine. Next, I tried one of the backups that came with it, but it didn't work. There was a cartridge that came with it though, called an ST-Key or something which is meant to play other region games. I inserted it in the cartridge slot and tried running the backup again, and it worked!
The Saturn booted up normally, but after seeing the screen say ST-Key v 1, it then went to the Saturn menu screen. Then, I could just press start and the game would boot. I tried all of the 20 backups that came with the Saturn and several that I've burned this afternoon, and all worked. To test it more, I removed the ST-Key and tried runing several backups, but none would work.
Although I'm new to running backups on Saturn (even though I used to own a Saturn before and I only played originals), maybe I've overlooked something here. It seems to me very much likely that this ST-Key lets me run backups without a mod.