No, the glass is not the digitizer. The digitizer is attached to the back side of the glass (adhesive) and is extremely difficult to remove. When I have replaced these on iPhones I always purchase it pre-assembled because I don't want to mess with applying the digitizer film to the glass (it has to be perfect).
If he searches digitizer with bezel assembly on ebay, he's going to find exactly what he needs. I know what you're talking about because I've repaired about 5 different iPods, but even most dealers on eBay just have it listed as the digitizer.
