I’m not sure critical thinking is at fault here. I think there is a certain skill set to evaluating claims online just like there would be a skill of evaluating authenticity of a piece of art, but critical thinking is essential in applying either set of skills.
Perhaps the danger is just in hubris, as the article hints. People assume their ability to navigate other areas grants them automatic expertise in the online arena as well.
I also think there is a lack of awareness of how dishonest people can be online without reprisal. If people tend to look for certain things to verify if a website is legit, you’d better believe the people trying to dupe you have figured that out and imitated it. A website is not a peer-reviewed journal.