The tradition thinks of the stomach as a pot and the spleen as the fire under it. Food goes in, is cooked, and the steam of it, the tradition’s word is essence, rises to feed the rest of the body. A pot works by being warm. Pour cold water into it at the wrong moment and the cooking stops until the fire has caught up, and in a body whose fire is already low it may not catch up before the next meal. That is the entire argument, and it is a good one for the person it was made for.
It was made for the cold-and-tired person, and for everyone at mealtimes. It was not made as a law of physics. The classics themselves ask for something milder than the modern rule: not hot water, but water that is neither scalding nor chilling. A healthy adult who drinks a glass of cold water on a July afternoon has broken nothing, and a person who scalds their throat with boiling tea every morning has followed nothing.