OK, I left so many comments in here that I thought I better provide my own answer.
The "300dpi" rule-of-thumb comes from the world of offset printing.
4 color offset printing uses something called a line screen to create a halftone pattern of evenly spaced, but different sized dots.
Offset printing can typically print up to 2400 dpi or even much higher. However, that would be only when you're using 100% of a color--so there'd be no dots. So for text and flat line art, you would want to send an image at that resolution. This is usually handled by simply being a vector image.
For photos, however, because they are continuous tone, to print all the color variations of a photo, they have to turn it into a halftone, and the process of turning it into a halftone means it only needs a certain amount of data, that being typically 300ppi. You can certainly send a 600ppi image to the printer, but you likely won't notice any difference when printed due to the conversion to a halftone.
Example of a halftone image:
Now, all of the above refers to commercial offset printing. Inkjet printing is quite a bit different. Most ink jet printers use stochastic printing. Instead of a halftone of evenly spaced but different sized dots, stochastic printing uses all the same sized dot (very small) and varies how many it puts down in each area.
Because of that, high-end ink-jets can print photos much better than most offset printing can. And, because of that, you can often send much higher resolution photos to the printer and see a difference.
As for why this printer has a different resolution in each direction, that's due to the mechanics of the printer. Many ink jet printers can print in a higher density in one direction than the other.
Example of a stochastic image:
(Both sample photos are taken from this pretty good overview of how ink jet printing works: http://www.thetonesystem.com/inkjet_basics.html )