Tons of rooms in the house have a hot water tap. Downstairs is the kitchen, laundry room, maid's room with her bathroom and a powder room. On the 2nd floor there are 3 bedrooms each with their own bathroom.
Our house has hot water taps everywhere too - hate to tell you that it doesn't mean there is proper/separate piping to the hot spigots.
Even our little house was built with the set-up and wall switch for hot water though, hard to believe one like yours wasn't. Do you see a light switch outside any of the bathrooms that has a little round red light about the size of an m&m in the center?