I remember hearing the older song on a great soul/funk show our student radio used to have, so I googled the lyrics, and came up with essentially nothing (usually searching for text passages is a great way to find stuff; my girlfriend catch plagarists in her classes this way. Moral: kids, plagarize from books, not the internet).
From what I could find out, the phrase is just something people said. There are cheerleading versions ("…we don’t need no water, let the spirit rise higher") and (maybe?) protest versions ("…we don’t need no water, let the mutherfucker burn"). Also, Tha Eastsidaz, Coal Chamber and who knows who else use the lines on records.
Google turned up all sorts of non-song related uses, as well as the phrase in live (unecorded) call-and-response hip hop sets. The DJ/MC would yell, “The roof, the roof, the roof is on fire” and the audience would respond, “We don’t need no water, let the mutherfucker burn”, so it must have been a phrase people just knew, circa mid seventies or even earlier.
Maybe if someone has the Bloodhound Gang record, they can tell us if the funk song is cited in the liner notes. Probably not, though, since they just alluded to it, rather than sampled it.
We don’t need no water
'Cause it’s an electrical fire,