I know that both component and DVI will pass 720p and 1080i because I've done with both. DVI should also pass 1080p just fine, and while in theory 1080p via component is feasible you run into the problem of practicality. The only 1080p component source I know of is the Xbox360, and the only way to display 1080p via that output that I ever heard of was a VGA connection - the component inputs of HDTV's pretty much universally are limited to 1080i input.

I'd wager that they are recommending DVI/HDMI for HD video sources because almost all HD displays today are digital devices, particularly when it comes to displays with a DVI or HDMI input (my trusty CRT HDTV is something of a freak of nature in this regard). As a result, keeping the video in the digital domain from source (DVD, HD-DVD, Blu-ray, cable/satellite, etc) to the display (DLP, LCD, LCoS, etc) makes a lot of sense.

IF you are getting anomalies with HDMI, I'd check the cables first. HDMI retains DVI's cable length limitation (a restriction that didn't matter a bit for desktop PC's but starts to be a bit mroe of an issue when you get into home theater setups), and that restriction often shows up as white "sparklies" or other artifacts in the image. Add up what the overall length of DVI and HDMI cable is from source to display. Also, you can get bad cables from time to time and replacing the cable can fix matters. That could be tested by swapping cables around a bit to see which cable the problems follow.