Stuff that is okay for people in the water is not necessarily okay for fish. Even clean water can have harmful things.
Namely, phosphtes and nitrates, which corals and inverts can't tolerate, and can lead to algae problems. Tap water usually has these at low levels, but in some areas it's bad.
Tap water also commonly contains metals. Or if you have copper plumbing, it will contain some amount of copper. Copper is fatal to inverts and corals, even at very low levels.
RODI water will have TDS (total dissolved solids) of close to 0. Tap water commonly has TDS in the hundreds (where I live, 400 to 500 is normal). That's all crap that you don't want in your tank.
Now, some places have good tap water, but I'd still recommend using an RODI unit to take out all the stuff you don't want in your tank.