The article doesn't need to prove anything, other than cite the study, because it isn't science. It is just news about the science. I am sure that the study itself, which was made by scientists and published in a scientific journal, would actually show their workings; otherwise they would not get published. But the fact that we haven't seen the study is not itself evidence that the figures were based on "no science what-so-ever".
If you walk into a room with your eyes closed, you cannot definitively say that there isn't a red ball in the room. All you can say is that you can't see a red ball. Similarly, if you haven't read the paper, you can't say that the percentages are unproven. All you can say is that you haven't seen the proof.
Should the original poster have read the study before discussing the percentages? If this were an academic discussion or an official policy document then absolutely. But this is just a forum on the internet, occupied by deniers who make no effort to prove their own claims. Regurgitating figures from the article is a step up for a lot of people around here who never get past reading the headlines.