I think you are conflating popularity of an argument with popularity as part of an argument. For the former, it's easy to agree that it does not affect the correctness of the argument. But in the articles case, popularity is part of the argument: That it is especially worrying the speaker is uninvited for an opinion which is held by a majority of people, i.e is popular.

Another example of this would be if we were having an argument about what music to play at some event we are hosting. I might well use the popularity of some songs as an argument.