Checking the oil is the owner's responsibility. My owner's manual says that I should check the oil level at every fill up. I've since discovered that means checking it every week. Not a big deal.
It's also good to look inside your engine compartment, and familiarize yourself with how everything else should usually look. This can save some heartache and money too by allowing you to prevent an issue from becoming a disaster.
When I was at the Dragon in September, I was looking under the hood every day, because of the intensity of driving. One of those times I noticed that the clutch fluid reservior was nearly empty, and there were signs of leakage around the cap.
I immediately went to a local auto store, bought $5 worth of DOT 4 fluid. After filling it, I realized that one of the mechanics must not have screwed the lid on properly, and the fluid was leaking out as a result. It was fine after that.
Who knows what could have happened, where I could have been stuck (middle of nowhere), and the towing bill I would have paid. Not to mention the lost time dealing with all of that, instead of enjoying my vacation.