I can respond from the automotive end of the world. I have been employed by a major import auto manufacturer for many moons, and I can say that customers who use genuine oil and fluids certainly are treating their vehicles better. But the warranty requirements, in our case, do not call for only genuine OE fluids to be used. More important by a long shot is following the manufacturer's maintenance schedule. As long as the frequency of oil changes etc are maintained, and records of such are kept for review (work orders, receipts of supplies etc), then it's tough for any manufacturer to deny warranty, IF the failure is due to a defect in materials or workmanship at the factory level . Some "warranties" these days for other types of producsts cover such things as damaging an item by driving over it with your car. More traditionally in any automotive or mechanical company (like tractors too, I would suspect), the warranty covers what is "deemed to be" (by the manufacturer, of course) a defect in material or workmanship.
So, I guess the short answer, IMHO, is that using the original equipment manufacturers' products might endear you to them somewhat if there is a failure that is questionable and might or might not be "warrantable", but it should not be REQUIRED to maintain the warranty, UNLESS it says so in your warranty book.
Manufacturers' representatives typically are looking for evidence that an owner properly maintained their product, and it's quite amazing to see how many people just don't bother to provide proper maintenance for such expensive products as cars, trucks and tractors. We have even on occasion declined a repair due to a total absence of maintenance records and admissions of not having performed ANY maintenance ("gosh, the sales rep never told me I had to change the oil"). And when challenged in small claims court on the few times we have done this, the court has more often than not sided with the customer (""This is The People's Court and I think the Big Company can better afford the repair than the owner who drove the car for 4 years and never changed the oil").
Sorry to be so long-winded!! /forums/images/graemlins/tongue.gif