In older quests, swords that don't have sword beams on them do.
Example: In Trinity Worlds, I clearly remember that the first two swords didn't have sword beams. Guess what? I tried it out, and the first sword had sword beams.
Having sword beams when you're not supposed to is cheap. Even cheaper than cheating in Trinity Worlds to get the Lv. 3 sword by the level 5 boss.
Older quests w/o sword beams have them
This has been reported already by s2dve. 😉