Would those types of small injuries give rise to enough blood to make 2 bloody handprints?
Perhaps, IMO, maybe more so the dog biting him fiercely & not letting go & him having to work hard with force to unhinge the jaw of the dog. Prying, scraping, punching, it's too awful to contemplate & I'm a bit reluctant to go any further with this, it's just a theory after all.
I have had dogs through most of my life, though, and when they had an injury to their mouth from a fight (usually with another dog but sometimes with wildlife or rodents), they bled from the mouth quite profusely at first, mixed with their saliva, and it got bloody right around their mouth.
When we would consult with a vet, they would say to keep an eye on things and if they didn't stop obviously bleeding within a minute or two because minor mouth wounds heal pretty quickly in most mammals, to see if they would let us look at how large the laceration was, but stitches were not usually needed because their saliva worked like a liquid bandaid usually after a minute or two, and they would swallow most of it.
Apologies if TMI/off topic, mods please delete if so.
Just offering a perspective on the possibility TD's dog bit him, and my experience with blood getting on you for a bit when they get a laceration in their mouth and them healing up pretty quickly.
JMO