To be more specific, Precheck requires an integration to/from the TSA that is at least in-part separate from Secure Flight. While I am not an absolute expert, at a minimum the KTN has to transmitted to the TSA (which may be included in secure flight), and then the airline has to take a response from the TSA on whether or not Precheck will be on the boarding pass or not. Airline IT being glacial and expensive to customize, not all foreign carriers with flights departing from US airports have chosen to integrate.

It's also worth noting that GE or any other KTN source is not an absolute guarantee of Precheck, the TSA computers decide, which is why they enforce the requirement that the boarding pass contain the TSA's response on whether the traveler is given Precheck/standard/selectee screening.