I mean, think about it. Say you have a 600dpi printer. Take a typical web page that sets its body element to be 1000px wide, because the person writing it was using a 96dpi display. If "px" really meant "smallest controllable dot", that web page would print about 1.66 inches wide. Which is obviously undesirable. On the other hand, if "px" means "the length that looks about as long as one pixel on a 96dpi display" then the same web page would print about 8 inches wide, which is probably much closer to what both author and user wanted.
This is also exactly why Apple did the "pixel doubling" thing on iPhone 4 and iPad 3: it was done to prevent existing content that made certain assumptions about the visible size of "px" from breaking.