Can I Replace the Digitizer without Replaceing the LCD?

I am trying to repair a black AT&T iPhone 4.

The front screen & rear glass panel are both shattered.

I know (thanks to iFixit!) how to replace the rear panel, but I'm stuck on the front panel: I've heard that it isn't possible to simply replace the digitizer on the iPhone 4 (because the LCD is permanently attached to the digitizer) but that you have to replace the entire display assembly. Online I have found iPhone 4 GSM digitizers for $30+, but the iPhone 4 GSM display assembly is $120. Can I simply replace the digitizer, or do I have to replace the whole display assembly?