There is an important distinction to be made here, as there is ambiguity when you talk about “authors posting PDFs of their papers”. This can mean a PDF of the paper as it was published in the journal (on paper or electronically), including the work one by the journal’s editorial and publishing staff to format it nicely, to use their preferred fonts, columnation, etcetera - or it can mean a PDF of the manuscript the authors submitted for publication (the final version for typesetting, I’m not trying to claim the journal has copyright over changes the authors made in response to peer review or editor’s comments).
The journal has a very reasonable claim to the version they’ve paid to format and branded with the hallmarks of publication in their journal and likely with their logo; they have (or should have) no claim to the manuscript version. Critically, if the linked article even mentions this distinction, I failed to notice it. This means that I don’t even know which version of the manuscript Elsevier is demanding be taken down in this instance - but, generally speaking, it is my impression that journal publishers don’t interfere when people post their manuscripts online, as opposed to posting electronic reprints of the version the publishers formatted.
