Hm.
CLAY
The brown (or black) "crud" is not "crud".
It is clay.
Over-mixing (and time) seems to churn out the clay particles.
Google why clay has trace elements. (It's an interesting topic!) Clay is basically used as a carrier. Saltwater apparently makes most trace elements dissociate from the clay – very convenient for us!
Tropic Marine yields black and IO/RC yield brown, BTW. (Not sure on other brands....these are what I'm familiar with over-mixing.)
I've never seen either a brown or back residue when saltwater is NOT over-mixed, for what it's worth. (I am also familiar with *not* over-mixing TM, IO and RC.

)
CRUD
The crud people are talking about is (mostly) calcium carbonate precipitate. This is coincidental (and mostly unrelated) to the brown/black clay buildup some people see when over-mixing.
Instead, crud is related to the supersaturation of seawater and the limitations it has.
I think Randy's already linked his article on "what's that precipitate?" which, if memory serves, addresses this pretty well! :) But in summary (from memory), excess agitation and heating presses on the limits of a supersaturated solution like seawater.