Global Entry is a program for entry into the US from all countries. Nexus is for Canada from all countries and from Canada into the US. Since when is Canada able to process Global Entry? I've seen no indication of it. (From global entry's web site): "How Does the Global Entry Program Work?
At airports, program participants proceed to Global Entry kiosks, present their machine-readable U.S. passport or permanent resident card, place their fingertips on the scanner for fingerprint verification, and make a customs declaration. The kiosk issues the traveler a transaction receipt and directs the traveler to baggage claim and the exit." There is no way for the Canadian officer to access the fingerprint record.