Hi John,
There is no fast/definitive answer for this situation, as trying to receive and demodulate a signal in the presence of another interfering signal is difficult, and depends on many things. So here's some suggestions.
First, have them perform the same tests using the CC1020EM running under RFStudio, or better yet, interface the CC1020EM in their system, use it instead of the pcb design of the end product. This will help determine any pcb layout issues that may aggravate the situation.
Next, see this App Note on Spurious Emissions, esp the sections on PLL and section 4.2.2 on blocker rejection, and by using a lower Ref Freq can improve rejection: http://www.ti.com/litv/pdf/swra057.
Of course using the RSSI indication for channel activity, and then switching to a different channel is always a possibility, although some protocol code changes would be required; this App Note is a good reference: http://www.ti.com/litv/pdf/swra062 .
Finally, doing a redesign to the CC1120 might be an option, as this is a newer, higher performance device: http://www.ti.com/product/cc1120 . If they are willing, get a CC1120EM, perform the same tests as with the CC1020EM and the actual product, then compare results. I believe the CC1120 will provide the best performance.
-Leonard
Analog Applications - ACAT Dallas