Yes they can include mechanically separated chicken, which is basically a fancy name for saying they scraped all the meat off the bones. But that isn't "mostly skin and cartilage", it's meat. There may be trace amounts of cartilage and small amounts of skin in it, but they are nowhere near the main components.
If you're still not sure, just look at the protein content of chicken nuggets. The quantity of protein can only come from actual chicken muscle. Skin has little protein and cartilage has virtually none.
There are a lot of urban legends out there about what chicken nuggets are made of. But they're precisely that -- urban legends. They're false.
Seriously, do you think researchers are wrong on this?
Meanwhile, other studies show that inclusion of 40% mechanically separated meat does not change the appearance, taste or desirability of chicken nuggets. Do you really think the majority of producers are not going to turn that waste stream into more product and profit?
In the United States, mechanically separated poultry has been used in poultry products since 1969, after the National Academy of Sciences found it safe.