The funniest part about the osha-offical Tumblr account is that they got banned because it turned out they had nothing to do with OSHA and were just really passionate about workplace safety.
Technically given that this seems to be a squirrel and they basically don't take fall damage I'd argue that they aren't required to wear one as they'd never be actually at risk of injury from a fall.
I'd actually think there's a pretty strong argument that getting caught from a fall by a harness would be more dangerous to them than being allowed to fall freely in almost all circumstances as long as the work space is clear of hazards they could fall onto.
The photo could be misleading. Are you sure the squirr employee isn’t stationed underneath an oak tree? Surely falling hazards exist under the old oak tree.