I can think of a few other ways to " fold a fitted sheet", although this would require a little" out of the box thinking "which I am sure some Vets can figure out...
I've found the easy way to never have a less than a perfectly folded fitted sheet in the linen closet. Buy one set of sheets and make the bed. Remove, wash and remake bed with same sheets. Saves space too.
Otherwise just roll them in a ball and put behind the perfectly folded towels.