It’s not double work, it’s the proper amount of work to do the task you (should) want to do: share information in an accessible way. Also, there are a billion different ways you can create decent HTML and a PDF from one source.
They're saying that because browsers render the HTML/CSS differently, the prints wouldn't look good. I don't think this is necessarily true, but even if it is, CSS lets you style the print version of a page directly so that the print looks good, and you can even make it look like a normal document and not a printed web page
