Go to this pdf, and scroll down to page 22 to see the diagram of the EGR system: http://www.motorcraftservice.com/vdirs/diagnostics/pdf/obdsm986.pdf It shows the EVR (EGR Vacuum Regulator) which I theorize, if its diaphragm had a hole in it, could allow fuel-rich intake air (partial vacuum) to reach the EGR valve.
At any rate, all the parts which operate on, and with, the EGR valve need to be checked for proper operation. This includes checking the tubing for carbon build-up, and the orifice opening for being open.
You can download, and print, these pages for “clarification” for your repairer. I hope they are receptive.