What the author misses is that with colour LCD displays you can do sub-pixel anti-aliasing with the 3 RGB sub-pixels, if you start from a vector, which is why HTML type looks better than Photoshop rendered type.
I purposefully chose to ignore subpixel antialiasing because it's complicated and you have little control over how it works. It's done at a layer further abstracted from the source file, so you can't accurately pixel-fit anything to a subpixel. It's also just another hack, using a smaller unit than a half-pixel, and, like most hacks, it has some serious negative side-effects.
He's not suggesting that you subpixel antialias manually. He's pointing out a benefit of leaving your images as vectors: the browser knows the subpixel order of the display, and can make the image prettier than you can without that information.
It can make it effectively higher-resolution than you can, but that doesn't mean it can make it prettier. It could still look end up looking worse (from the color bleeding effect, for instance).
You can't even reliably fit raster images to screen pixels on the web. Images can easily end up at non-integer screen pixel locations which requires resampling (and ruining your careful alignment) to render.
Logo design should be done in-context, not in a dark room at 400% zoom.