Why would a large resistor in series cause a different voltage reading?
The equivalent resistance of a group of parallel resistors is always a number smaller than the smallest individual resistance in that group.

So you can see here than as long as you introduce your body as a parallel resistance to anything after a resistance in series with the source, the total resistance seen by the source will decrease causing more current to flow through the series resistance which drops the voltage more than it otherwise would at the point being measured in the middle of the divider.

If that series output impedance is very high the it does not take much additional current to cause a huge voltage drop across the resistor. The multi-meter is designed to have a high input resistance in order to minimize the additional current flow which would distort the voltage readings. But your body's impedance is much lower.







simulate this circuit &ndash; Schematic created using CircuitLab

EDIT: I added in resistances to show when the water is a continuous chain from the showerhead all the way to some ground point (maybe the faucet or pipes) and when the water stream is broken.