I think the point they were making was not to stop doing science, or publishing. Instead its the problem with the reporting of science. Everything has to have drama and conflict.
The news makes it seem like every new paper is a paradigm changing event. Where as from the point of view of people who are doing this work its another piece of information to help improve our understanding.
The biggest problems is when popular news makes people think science is just stories, it seems to change every other week from one extreme to the other, so with overwhelming scientific facts like evolution and climate change people think its just some "theory" that is just as likely to be proven wrong tomorrow.
Its a difficult balance to find the best match between the public's hunger for science news and the sensational nature of reporting.