They don't have to give it away, but if they publish it so that someone can view it, then others who can view it should also make their own copy to do what they

They don't have to give it away, but if they publish it so that someone can view it, then others who can view it should also make their own copy to do what they want with, e.g. adjust volume, make a recorded copy to work without internet connection, convert file formats, downgrade resolution (if you want to save disk space), time shifting, deleting ads, etc. It isn't the problem that the site doesn't have a download; it is that the computer should have a record button but doesn't.