I don't think anyone would say the FoMoCo fan came as original equipment on the Skylark. Back then GM very rarely allowed branding of component parts unless supplied by a GM division. Notable exceptions would be things like tires and Hurst shifters.
Aftermarket parts suppliers, even those owned by carmakers, wanted to sell their parts to anybody and everybody through retail parts stores. For example the Delco Air Conditioning Parts Catalog has lots of listings for Ford, Chrysler, AMC etc. The 1974 edition has a line of universal "Centri-Flex" radiator fans for all car makes. The part number for a '68 Buick Skylark is also given for numerous Ford cars.
Attached are a couple of pages showing tips on installing the universal fan blades. There should be an original 2" long spacer present between the fan pulley and fan blade. The spacer keeps the blade in the same position it would be if the car had been equipped with the thermostatic clutch.
No doubt there is a FoMoCo aftermarket catalog somewhere showing one of their 18" 4-blade fans fits a non-a/c '68 Skylark. If the FoMoCo fan meets the installation guidelines and prevents overheating, it's doing the job. Worst case operation would be idling in gear in very hot weather.