Canadian-Turkish dual-citizen traveling with Turkish passport and Swedish residency card when taking common carrier flights from the US to Sweden (or elsewhere in the Schengen area) worked with the airlines. Just don’t expect it to fly with online check-in or kiosk check-in since the check-in counter agents — and sometimes also the gate agents — did manual reviews for visa exemption and then proceeded. And nowadays there is also biometric exit/boarding to be considered in terms of what that means for such situations.