I don't think that's the case at all. It isn't a black and white issue, and I certainly don't feel it has been conclusively shown that if I start drinking drinks that are BOTH fizzy and sugary tomorrow, it will result in my telomeres shortening at an unusually high rate as the article claims. Is that really anti science? I don't think so.
And lay folk do find errors in papers all the time, it varies a lot on the paper and the field how difficult that is though. Some papers, the vast majority of scientists would not be able to spot errors, it really depends on how specialist the required knowledge is and there really are no hard and fast rules there.
So given a study that turned out to be false, in general it isn't possible to argue either way as to whether a layman would spot errors, you would have to argue it on a case by case basis.
The one thing we do know is you definitely cannot spot errors without at least reading the thing and going through the working.
Ugh. Another blanket statement that in no way reflects the actual paper in question.
From your own source he recommends larger studies, cross-team work clear pre-trial hypotheses, and study-registration.
Guess what?
This n=5,300 study was performed by researchers at UCSF, Stanford, Berkeley, and Michigan, they published their intention to run the study prior to running it with a hypothesis that was partially proved wrong (they expected shortened telomeres with noncarbonated SSBs as well as with sugary soda).
What exactly is your issue with this study? Or do you just reject science in general.