Under the Magnuson-Moss Warranty Act (do a google search), a manufacturer cannot withhold warranty repairs for not using a specified product unless they provide the specified product free of charge. In this case, dealing with oil, as long as it meets the mfr's requirements (CH-4, etc..), and is of similar weight range (say you're using 5w-40 in lieu of a specified 10-30, for instance), they cannot deny warranty work on that basis. A lot of dealers make a LOT of money selling "genuine, OEM parts", that are actually made by somebody else anyway (does Kubota, John Deere, etc.., actually make their own oil or filters?) and re-packaged in OEM containers.
We got into a similar situation with some of our Toyota pickups back in the late '80's that were having head gasket problems. The service manager at the Toyota dealership noticed the oil filters were not OEM (we use WIX/NAPA), and tried to get out of doing the repairs until we mentioned M-M. His tune changed quickly. As it turned out, there was a bad batch of thermostats out there which caused the engines to overheat and warp the heads.