That's making a lot of assumptions about the plumbing. Especially considering that a lot of public toilets and even hotel indicate that water from the tap is not safe.
For a practical example, in my old flat, the bathroom tap was hooked to the cold water tank that fed the hot water tank, hence potentially unsafe (definitively unsafe before I cleaned it after changing a valve). The kitchen tap was taking water directly from the main. That is BTW quite a typical british setup.
This is getting less common in the UK, usually when a new combi boiler is installed the tank is removed / uninstalled.
But in general it's good advice for the UK as expansion overflow from the hot water system went back into the cold tank (also there might be dead wildlife in the tank).
I think there used to be restrictions about connecting mixer taps directly to the water main (I suspect this changed sometime in the late 80s / early 90s) as I remember a friend getting his shower replumbed so he could get mains water pressure in the shower and it seemed like a newish building regulation thing.
I think virtually all new installations are mains water pressure throughout.
For a practical example, in my old flat, the bathroom tap was hooked to the cold water tank that fed the hot water tank, hence potentially unsafe (definitively unsafe before I cleaned it after changing a valve). The kitchen tap was taking water directly from the main. That is BTW quite a typical british setup.
Anyway you are probably safe regardless.