I bought a used copy of Ico from Gamestop (I know, I know...I deserve whatever I get) and ran into a read error halfway through. By that time the 30-day return period had run out, so they won't take it back.

Anyway, I took the disc to a local used CD/DVD/game shop for repair, and they told me that scratched PS2 games can't be repaired. This is the first I've heard of this, and the clerk at Gamestop said they'd buy it from me (for $4) and send it in to headquarters to be repaired. I assume they'd have a policy against accepting damaged discs if they really couldn't be repaired.

Can they be repaired, or not? Does anyone have any suggestions regarding where I might take it for repair?

My personal recommendation is just to buy a copy off eBay or somewhere that is in better condition. It will cost you more, but it will also save you the hassle of trying to find a place that will repair the disc.

This depends how deep the scratch is.  If it's a deep scratch, you need someone to buff it down, but you shave off plastic in the process.  It may be that the PS2 discs are very thing, so any buffing would expose the data layer itself.

Light scratches should be repairable with the usual methods found in video stores.

Its been my experience that DVD-ROMs scratch much, much more easily then CDs or CD-ROMs.  Not that that helps you in your current case (I too recommend finding one on eBay), but it is something to take note of.