This. I'm actually a bit puzzled about the OPs claim, that the DMG says otherwise. Does anyone have a page number for reference?If they were there, they participated. Just like combat.
Anyway, my tip:
Don't use traps. They suck. Really!
If you absolutely have to use traps, use encounter traps (detailed in Dungeonscape and iirc in some Eberron source book). At least with these everyone in the party can contribute.