The way it really works for plastic is this: almost all bad plastic is black, but not all black plastic is bad. That's it.
There is nothing wrong whatsoever with virgin black plastics. (Well, at least, nothing more than is wrong with plastics in general.) So there is no reason to fear black plastic from reputable sources.
The trouble comes in when plastics get recycled. There may be sourcing issues for black resins, but the root of the matter is this: black plastics are typically pigmented with carbon black. Carbon black as a pigment is cheap, safe, and very effective. That's good! But that also means that when you throw together a pile of recycled sludge mix and it comes out beige, greige, or worse, you can't sell that (who would buy greige resin?? wait, don't answer that)... so you color it, cheaply... which means carbon black. So almost all random crappy recycled plastic resin ends up black. That's the real problem with black plastic.