Were you ever able to figure out what is going on? I'm having the same problem in my house. When the hot water is opened all the way, we get this black greasy stuff left in the tub. It looks like little tiny specks at first and then smears around when you try to wipe it off. I give my 1 year old a bath every night and it doesn't show up then because I don't open the hot water all the way. I know there is no flexible supply lines going to the tub or coming out of the water heater. Everything is soldered copper lines.
Get rid of the magnesium anode in the water heater and put in an aluminum one. It is a chemical reaction with the water creating magnesium sufide. You have a water softener right?
This is awkward, but...
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