TL;DR: Retina render image in it's native physical resolution and is capable of doing it, but when content isn't Retina-optimised it performs extrapolation of content and images look blurry.
What I said about 4-to-1 pixel is, of course, a simplification.
Displaying any image that's not exactly the same resolution as the screen we're displaying it on will result in various distortions of original image.
Worse scenario out of two is upscaling or displaying low-res content on a high-res screen. Even with an integer coefficient, extrapolation algorithm won't just "multiply" image pixels because it'll look as if it came from Mario world. In real world some intermediate colours are calculated and the image looks slightly blurred (and pixelated, too).
Downscaling is slightly better because in theory you can collapse N identical pixels into N / X^2 (where X is the integer ratio) without losing any characteristics of an image. But the majority of content is not like that and interpolation algorithm would calculate an average of those N pixels while also taking into account some surrounding pixels. That'll also result in some blurring, though not as severe as in previous case.
That was for conventional screens, now back to Retina. Retina is a conventional screen to some degree, too. In most cases the content it renders is designed for standard-DPI displays, so it extrapolates it (1 case). But because Retina's physical pixel is much smaller, visible distortion effects aren't that severe and your eye is doing some amount of interpolation, too.
When designers add Retina-optimised images in their interface (2x images of elements on web sites etc.) they are rendered in native physical resolution and look sharp. But the amount of content on the screen is still the same as on conventional screen. So if I open THW forum on my 2010 13 inch MBP (1280x800) and on my friend's 2013 13 inch Retina MBP (2560x1600), we'll see the same amount of content (with the default display option for Retina).
There's also some other good parts about Retina that I've seen comparing the displays on aforementioned laptops and that's text. Not only it looks sharper the way it should look, but when you're going down the size scale it stays readable longer. We're both programmers so we compared the amount of lines one could fit in the vertical space of text editor using Menlo font. I prefer coding with font size 12 but can tolerate font size up to 10. 9 and less, it becomes a little blurry and at the size of 5 I'm beginning to guess what's actually written. On Retina I'm still able to see the text clearly at the size of 5 and probably 4.