The several WMs nearby have oil on the shelves. I would not say it's a lot. I would fairly say that the typical WM has about 25% capacity on the shelves. Some, like diesel, are almost entirely empty. For gas vehicles, big empty spots, and for the full spots, about 1-3 deep out of the possible 5-deep rows. There's probably not more than a few weeks of motor oil product.
It wouldn't take much to be cleaned out, maybe a week of non-delivery IMO. Or a oil price shock, say it jumps to >$100 barrel.
Having said that, there's probably 6 WMs in short driving distance. Plus there's at least 3 or 4 major auto parts retailers with probably 3-5 shops all within 20 miles, and they have nearly full shelves (because their prices are about 30% more than WM). So it would take a lot to clean out WM, and then clean out the ~15 nearby auto parts stores (which charge a premium). Plus, there's 50 auto shops in the area which all have bulk oil.
So, I sorta go back and forth on this. I'm sitting on thousands of quarts of oil that I've been having difficulty selling at 3/4 of what WM charges. So the demand is surprisingly soft, to be blunt.