Definitely the water - I had this in my previous house which had a loft
CW tank. As well as the gunge I had what looked like a few bucketfulls
of sand in the bottom. Taps fed from the tank used to regularly eject
gunge, and the cats' water fountain which was filled from the bathroom
taps (don't ask, fussy cats didn't like the high chorination in the
mains water) used to get gunged up regularly too.

Thing is, when I moved to a house with mains cold water only, I still
get the black gunge forming on shower heads, taps and the cat's
fountain so in my case it's definitely in the water.

I'd just leave it - it'll only come back again anyway. You could use a
less dangerous way to sterilise it, like Milton.