I see nothing wrong with any of the statements. The side "boiler" we hoped it did not boil the water, on the Aga stove, was piped the same way as Willis. Today we use a hot coil, and the water in the boiler is not the same as water behind the hot tap, but in 1954 when parents house was built it was.
But I can't remember how long from lighting the fire it took to get hot water at the taps.