"Water heater case was rusted through near the drain, and there was rust around the pipes and other case openings. I suspect it was venting in the space between the tank and the case, and combustion byproducts were leaking into the room. Recommend water heater be replaced as soon as possible by a competent, certified, and insured plumber.
Byproducts of natural gas combustion include carbon monoxide, a poisonous, colorless, tasteless, odorless gas that can be lethal. The condition of this water heater indicates that these gases are not being expelled properly, and need attention now."
It looks to me like the flue inside the heater is blocked somehow. I couldn’t see anything inside the chamber, but it looks to me like the exhaust is travelling in the insulation space between the tank and the case.
Sounds good to me, you could add “this tank likely went bad many years ago” so they don’t try to squeeze another few years out of it in order to get some new drapes or granite tops. What is the age of that pile?
A backdrafting dryer would put heat, moisture, lint, and in the case of gas dryers, exhaust back into the room. A water heater would draw them in as it is firing for combustion air and through the draft diverter. Am I understanding how it would happen?
That’s not the case here, however, as the only other appliance in the room is a direct vent furnace. The electric dryer is on the floor above and vents to the attic (a whole different issue).