Some manufacturers can be more/less stringent. Subaru seems to be less of a hassle than Hyundai. Hyundai has somewhat of a reputation for denying things if you can't prove it... However, I never let a company get away with anything. I made a warranty on a 18 year old Subaru. They fought me on that. However, Subaru explicitly states that seatbelts are lifetime warrantied parts. Next, they fought me claiming that a dog chewed the belt. It frayed badly but every vertical thread was untouched (it was unweaving itself) and that the pristine leather seats showed no dog issues. Then again, Subaru denying something over a dog is a bit anti-corporate image.
One, I purchase oil/filters (as well as any other PM items) for my "under warranty" vehicles online (Amazon). Thus I have an automatic receipt archived in both my email and Amazon account. No worries, I still have a lot of clearance oil in my stash.
Next, I use the "MySubaru/MyHyundai" (OEM's website tool) online maintenance reporting options. Thus, I have a record with the manufacturer (timestamped) when I do maintenance. You can also see other dealer reported work if it was done.
Next, I take pictures while working. This is more for the "inspect X, Y, Z" elements of the service schedule. So if I have to take something in because X failed, and the dealer says "nope" because you did not check it, I have receipts, reporting and photographs that can prove otherwise.
Finally, I keep any other receipt/documentation tucked in vehicle specific binders. Normally, I am a bit lazy here so I only really file things once every 6 months and in the mean time they are stashed in my MR2 service manual.