There are 2 assumptions that can be made. Body is insulated or body has good connection to earth. Worst case of those two is good connection to earth since if the body was insulated we could handle lives wires with no problem. So with that assumption, for safety, any other metalwork should be obviously isolated or failing that bonded to the same potential as the body.
It's a bit more complicated than that, in as much as the body may be connected (or not connected) to different things at different times - but, yes, in any environment (not just bathrooms) the risk of electric shock can obviously be eliminated by ensuring that everything touchable is at the same potential.
However, as I've said, I think a degree of common sense is required in deciding what "realistic" risks there are of metal objects (pipes or whatever) becoming 'live'. As I've said, the (incredibly small) risk of that happening is probably as great (maybe even greater!) in the case of a screw holding up a bathroom shelf or (maybe metal) cabinet as it is with a water pipe.
That would be my guess at the reasoning behind treating bathrooms as special cases. Otherwise, if you take water as immaterial and the body as insulated why treat bathrooms as special?
Good question - and, as with some other regulations/requirements, it might well have been a 'knee jerk' ("electricity and water don't mix") based on theoretical considerations, without any real evidence that electric shocks were any more common and/or any more serious in bathrooms than anywhere else.
I suppose that the most obvious reason for singling out bathrooms is that it is a place where people are frequently naked, with no footwear and with very wet skin (hence low body resistance). Hence, if there
were (for whatever reason) any dangerous potential differences around, the risk of any resultant electric shock being 'serious' (perhaps fatal) is greater than in most other environments. Don't forget that until quite recently kitchens were lumped together with bathrooms as 'special locations'. However, that was dropped, quite probably because they realised that the (usual!!) absence of wet naked bodies in kitchens meant that they did not justify/require any 'special treatment'
BTW when you tried to measure resistance in a flow of water what did you use? For liquids (and gases) the voltage will be important. Water needs a couple of volts to get the current flowing.
It was a good few years ago, so I can't recall the details. However, I wouldn't have used a very low voltage, for the reason you mention. I almost certainly would have used an IR meter, in which case the testing would probably have been at 250V, 500V or 1000V (probably all three). If/when I have a few spare moments, I'll try a few more experiments!
But if the water is falling then it will likely split into droplets so have air gaps and thus no continuous path.
That was, of course, my very point. In fact, because of cavitation, air bubbles etc., even water flowing within a pipe can be far less of a 'continuous tube of water' than you might think.
Kind Regards, John