If you turn on the cold tap from that faucet, would you get hot water out? That sounds like the awful nightmare of my childhood summer camp's shower system, wherein the cold water supply would often become blindingly hot, even if you had the hot tap completely closed. Since then, I've always wondered how you're supposed to engineer a building's hot/cold water system to avoid this sort of thing. I figure it involves having staggering amounts of positive pressure in your pipes such that you'll never get any sort of backpressure, but what if a clogged faucet effectively shorts the hot pipe to the cold pipe? I've likewise wondered why somebody doesn't make a digital shower controller to maintain constant temperature through transient pressure drops (e.g., toilet flushes). Ahh, the things you think of when you're stuck with inferior plumbing.