I thought of a couple of other things, but they are obscure.
Call your water utility and ask them if they have check valves on your waterline. They often aren't perfect, but usually work. That's important if there is one and you don't have an expansion tank in the home. Usually, the water pressure when there's a check valve and no ET will peak after using some hot water and the heater turns on, but not if there's an ET. If there is a check valve, no ET, during water heating, that extra water pressure from expansion may be pushing water back into the supply line rather than causing the T&P valve on your water heater from releasing.
If you're certain that the meter isn't moving when you hear the noise and it really is water, some squeezing back through the check valve could cause it.
A second thing, if you have a pressure reduction valve and it has a bypass, and no ET, it will allow flow backwards, too, and may not build up enough pressure to open the safety valve on the WH (the T&P valve).
Both of those are related to the WH running. See if there's any correlation to the noise and hot water use previously versus say just cold.
There may be other things I haven't thought of...but let us know what you find...it might trigger some other thoughts.