It depends on WHICH console you own. DUh! I just played the game in that video yesterday (Final Fantasy X) and it looks infinitely better than what the video suggests.
http://www.engadget.com/2006/12/13/ps2-ps1-480i-games-hampered-by-crazy-jaggies-on-the-ps3/
"Infinitely Better".
Of course, to be fair, as far as I know those screencaps were taken before the filters were introduced in much, much later firmwares but you can still see the picture is pixelated and the colours are washed out - resizing always does that.
Furthermore, to actually get those video screen captures they would have to be using an emulator on a PC which means that they aren't even testing it on a real PS3 console.
That's how a screen capture device looks like. I know how you could get confused since PS3 emulators are so popular these days.
Backwards Compatibility originally worked on CECHA, CECHB, CECHC and CECHE PS3's, meaning on the PS3 Fat's.Even if they were, the video doesn't say WHICH PS3 console they are talking about. I'm sorry if you have a junk PS3 and/or a junk TV and/or don't know which settings look best, but don't take that out on me.
We're done here.
EDIT: Just so we're clear and there's no animosity going on, all I'm saying is that playing PS2 games is better on a PS2 which was made to play them, that's all. No hard feelings.