It really depends on the type of study it was, and what these sources of asbestos were supposed to have been.
If they were doing a comparison study, so long as the control group was exposed to asbestos in similar amounts and in similar environments, it's still a strong finding. J&J shouting "they were exposed to other asbestos!" would just be an empty attack on the researchers' characters, and an attempt to falsely discredit them to an uncritical and uneducated public.
Things do seem to be a bit more complicated than that, though, as these are post-hoc investigations with no control. That said, it looks like they tried to do their due diligence to filter out participants who had known environmental exposure to asbestos. If some of them lied or mis-remembered, then it's up to J&J to show that the researchers were negligent or operating in bad faith.
That's going to be a pretty big hurdle to climb. I don't believe they actually intend to climb it.
The fact that the researchers asked about environmental during recruitment, plus the fact that J&J is only claiming that a small handful of people involved in the study were exposed to other sources of asbestos, really shows this for what it is: An attempt to scare researchers away from doing research, and especially from agreeing to be provide expert testimony in lawsuits.
One of the defendants here even has a new paper out this past January that includes patients with known environmental exposure to asbestos, and they show that cumulative exposure from all sources matters. Including exposure from talc:
Conclusion
For individuals with exposure to asbestos through cosmetic talc usage and additional alternate sources, all exposures contribute to the development of mesothelioma. Published case reports and case series have identified over 100 individuals whose sole exposure to asbestos was through cosmetic talcum powder usage.
This finding basically cuts J&J's apparent argument off at the knees, and was published months before they ever filed suit. They'd have been aware of it at the time of filing. They don't seem to have anything here. Just the opportunity to try and make their detractors look as dirty as they are in the eyes of people who haven't read any of the research.