The researchers said they expect multi-walled nanotubes to also contain the contaminants, however the multi-walled variety are also much longer, so conceivably it could be their aspect ratio that cause an asbestos-like reaction (asbestos fibers are also very long, which causes them to get trapped in the lungs). That is why they have to text them next to find out whether its their aspect ratio or the contaminants.
I asked the researchers this question myself, but they said that many applications require carboxylation to functionalize the nanotubes, which produces the toxic byproducts. However, there are other ways of manufacturing them, and you are right to advise their makers to explore using those other methods (but in the meantime they should filter carboxylated nanotubes to remove the contaminants).
The title merely states the essense of the story, that reseachers say nanotubes are not toxic, which the story qualifies by stating that a certain kind have found to be nontoxic under certain conditions, and that those conditions are now being extended to the other types. This is standard journalist practice underwritten by the courts which do not require headlines to state the whole story, as long as the body of the story does.
The title and the first line tells completely different story. The title of this article says that Nanotubes are not toxic while the researchers claim only that Nanotubes may not be toxic. The whole article suggest the same thing that one particular instance of nanotube is found to be non-toxic but there might be other instances where it is otherwise.
We are not out of the woods yet, because the nanotubes that were said to be akin to asbestos were of the multi-walled variety rather than the single-walled ones tested here. However, they are looking at those now and there is no reason to think multi-walled nanotubes will also be given a clean bill of health.
I was surprised to think that there might be health considerations regarding nanotubes, so I looked up the previous article. Maybe we do actually learn from previous mistakes. It would have been very bad to have an equivalent to the asbestos fiasco all over again. Interesting stuff.