ROB:
Last try. OK? I spoke to an engineer (myself). OK? Please. Unless you don’t believe in science (another thread). Kindly. Tune in to this earthly world.
If you shut off the intake (cold water) NOTHING WILL EXIT – that is your “source of water from far away”. Unless you have air pressure, or hot line pump. Nothing. Again as I wrote earlier, not even wishful thinking will do it. (Maybe with a Shem – if you’re into those things)
Unless you are talking about a boiler on the same level or higher than the faucet – then of course one will have water equivalent to the level of the faucet.
Sometimes one may find some hot water still exists, thats a run from higher elevated lines, which will very soon cease. Or if you have a cross linked faucet, and open both, that’s cold water.
‘Know what? Why don’t you try it. Shut off (completely, no cheating) your cold intake. Open kitchen faucet (hot). See how long it takes to empty existing hot water from higher elevated lines. Then stand and wish for hot water to come. Wish harder, five minutes. Post results. (turn back on cold water, it could burn or bust if you don’t have proper preventive mechanisms)