You are correct. This article is misleading on many levels.
A CSS pixel is ALWAYS the exact same thing as a screen pixel, unless:
1. The browser's view has been "zoomed". This can occur on desktop browsers or mobile browsers, although it's much more common on mobile browsers.
2. You are on a quad-pixel display like an iPhone 4. In this case, 1 CSS pixel = 4 real pixels, exactly.
Options 1 and 2 rarely breaks anything due to a use of "px". Those situations that are problematic usually are due to a design flaw in your CSS (and will not be fixed by switching to "pt").
Option 2 will never break your CSS. The only time it matters is if you want to serve double-resolution images [1]. Other than that, you have no access to the super-grid, so don't worry.
[1] http://www.sitepoint.com/razor-sharp-images-in-mobile-safari...