The description you gave is only true if the application is resolution independent. If you take an excel spreadsheet, for example that was developed on a system with 13" 1024x768 screen and display it on a 13" 2048x1536 screen, everything will be 1/4 the size. Since we're talking about laptops, the icons are not automatically quadrupled in size. If you have your desktop set up on a Mac with current screen resolutions and then migrate everything to a display of the same size with twice the linear (4 times the area) resolution, everything will be 1/4 the size.
Applications don't handle resolution independence. Operating system does.