All of which makes for a well informed debate. The problem with the discussion is that you're not looking at the lines of reasoning that originally made the theory of a hybrid, more readily acceptable. The fish you named will all produce viable fry. Parrot cichlids do not. When you hybridize an animal you get mismatched numbers of chromosomes. This is how a mule can have very much the same characteristics, with every cross of a donkey and a horse. The cross itself creates a stable "stamp" of a look on the hybrid, but they are 99% infertile, duh to that mismatched chromosome. 1% are fertile though. This isn't a well known fact, because it would be a huge waste of time to attempt to figure out which of the 100 would be fertile, and then cross them back on one of the two types of parents, when you can get a fairly accurate copy, just by making the same cross again.
Occasional blood parrots are fertile, but usually only when spawning with some other form of cichlid, not each other. You hear stories of it happening, and technically it WOULD be possible, but I have yet to actually talk to anyone that's done it themselves and raised fry to see what they looked like, let alone seen pictures.
This, as much as anything else, is what has made the common consensus on these fish what it is, that they are hybrids, and not some form of true breeding mutant. If they were true breeding, they would be able to spawn themselves. Oscars, angels, and those other fish you named can, and when crossed back into less line bred forms, you strengthen and hearten the fry.
There is also another "parrot" type cichlid available in the hobby that I've seen marketed as "toffee" cichlids, that are obviously a convict/? cross, that they then dye. As long as people will BUY these things, they're going to keep putting them out into the market, IMO.
Barbie