I’m asking this for the nice people that lived next door to me 15 years ago when I lived in Olympia Washington. When I visited with them last September I notice in the garage ceiling had a good size water stain on the ceiling where the hot water tank vented. I mentioned it to him but other priorities kept him from checking into it.
This afternoon I had an email from him indicating there was water on the platform the hot water tank sits on. Not knowing where it came from he went into the attic area (tank is in the garage)to check for water.
He said there were no stains on the roof and the pipe itself wasn’t wet but the bottom section of the pipe going to the hot water tank is stained, the insulation was moist and drywall was like putty with moisture. (yes pictures whould be nice but I have none) given this information any ideas what is going on here. Obviously its been raining a lot in this area of the country, any clues given this. Any of you Washington inspectors got any ideas ? 
There’s really only two options from what you’re saying.
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Attic air is condensing on the outside of the flue and running down to the ceiling. Will only do it when the right temperature humidity conditions exist. I’ve even seen PVC plumbing vent pipe do this in my house.
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Roof leak around the flue pipe penetration. Pipe will only be wet when it’s raining. He needs to get up in the attic when it’s raining to see if this is the cause.
Water on the garage platform could come thru the ceiling but then there should be water on top of the heater. The location of water on the platform under the tank in the garage adds more sources, TPRV or water tank leak or pipe leak.
Elimination by trial and error.
If it ain’t raining, roofs don’t usually leak.
Water will also condense on the inside of a stopped up or non working flue.