How can someone may forbid you to save a personal backup copy of a publicly available document?
This whole thing is a can of worms and it may not be sorted out clearly and legally for decades, however, copyright (in the US anyway) means the rights to all copies, which includes digital. So if a site's terms of service and copyright notice says you can't save a copy of the site for personal use, then you can't do it legally.
Who's to stop you? Probably no one. But just because something is technically possible doesn't suddenly make it ethical. It would be technically trivial for me to shoot out my neighbor's windows at 3am with a pellet gun from 250 yards and be all but assured of getting away with it. Technology, ability, doesn't change morality.
The more respect--and peer pressure for continued mutual respect--we have for these sorts of things, the more open it can all be and remain. The more the windows are broken, the more the government cops have excuses to climb in and "protect" us.