BayRat, Was just checking... Well it seems even more likely the chemistry is the culprit. If the DHW tank were impervious to chemical assault you could fill it and let it cook with something really strong to clean out the deposits but that is not likely the case with most. This leaves 1. wait and see or 2. R&R the tank. Is there a problem beyond aesthetics? Will the "brown water" stain the sinks, ruin the fine china and crystal in the diswasher, react with someones hair dye, shampoo, or conditioner and turn their hair into a really weird fashion statement or selectively bond with tooth enamel to create a really horrific smile? If it is harmless aesthetics I would personally try a wait and see attitude or maybe a chlorine bleach chemical soak for the tank. If chlorine is pulling out the iron or whatever maybe you could accelerate the process by giving it a few gallons of chlorine bleach and a good long soak.
How to get the bleach into the tank? Hmmmm, maybe you could put a short length of hose on the drain outlet and place the other end of the hose above the tank. Put a funnel in this raised end of the hose. Turn off the supply valve controling the cold water coming into the tank. Open a nearby hot water tap. Open the drain valve and pour bleach into the funnel. Maybe as a confidence builder and safety check you could try pouring in water to make sure it goes in and doesn't overflow the funnel. In theory, the head of pressure from the hose and funnel above the level of water in the tank should force the contents of the funnel into the tank. Since many brands of chlorine bleach give water purification dilution information on the back of their labels it isn't too scary to put bleach in your water system. All the excess can be flushed out fairly easily through the drain valve and not put much into the house plumbing. The length of time you can let it cook is an issue. Planning an overnight trip or at least a day away so no hot water is used is a good idea. I would be inclined to return all valves to "normal" and have the heater in service as the elevated water temp will accelerate the process.
To get sufficient "head" you might have to take the end of the hose outside and use a ladder.
The down side to this is that if the tank has a potential leak that isn't leaking because of deposits in the tank plugging it, then this action could clean the plug away and start a leak. If the chlorine in the treated water is removing deposits the same thing will happen eventually but probably not while you are focusing attention on the tank. Either way, you might be replacing the tank if it isn't currently in good condition (without mineral deposits pluging incipient leaks).
Curious situation... Please post your actions and results, I'll bet it is of interest to several folks.
Patrick