Not too long ago there was a link on the house blogs main page to a toilet that had a small sink built into the tank. It would seem to be the perfect answer to the problem of people who want to add a first floor bath to their older home but only have incredibly small spaces (like under the stairs closets) to add a toilet. This way with a single supply line you could get two uses, and recycle water too. I didn't think much of it at the time, since this wasn't a need of ours, but really, if you did that would you want to wash your hands with cold water? Right now, if I went out and got one of these for our new upstairs bathroom we wouldn't have that problem, because we just discovered THE UPSTAIRS TOILET IS PLUMBED WITH HOT WATER! Without going into too many indelicate details let me just say that Lisa asked about feeling warm when she sat on the toilet. I stuck my hand in the tank, which had just re-filled, and sure enough it's hot water in there. Our string of good luck was bound to run out.
I have left a message with the plumber, we'll see what he has to say. My first thought would be to switch the lines at the basement, you could then cross over the supplies to the sink, but it gets difficult after that. The supplies to the tub are exposed, so hot and cold would be the opposite of what the faucets say, and the single lever shower would require you to pull it full bore (which would then be all cold) and ease it back to the right to warm it up. This is probably not acceptable.
However, we may have once again dodged a bullet. The supplies run to the upstairs via the closet in the first floor bath, and according to my measurements with Pete last night come up under the cabinets we put in the el of the bathroom. Those cabinets are held to the wall with screws, which we can back out,and remove the cabs. The floor under them is not tiled, or even covered with cement board. In theory the plumbers should be able to cut the subfloor, switch the toilet supply to cold, and put the sub floor back down, to be covered with the cabinets again. Stay tuned.