Actually..More specifically, thick as a brick is in reference to the net's ability to retain new training data.
When one is playing with heuristics, one can look at a bit of code and say, "That code does this here in that situation." Lots and lots and lots of code, but it's all visible; one can even get the equivalent of printf's on the state variables during debugging and all that.
My understanding is that, with a NN, all that visibility is gone. The natural design is that there's inputs, lots; outputs, not so many, but what happens in between might not quite be a mystery, but it's close. So, the question of, "Just what was it computing?" might not have any easy answer.