All your examples were about dogs overeating, which I don't think anyone would disagree dogs can do. But I think it's pretty rare for dogs to under eat and to need to trick them into eating their food.
I have no idea how you'd get "I'm in pain" from the associated body language; but, then again, I'm not a dog. In this case there were behavioural cues, but I don't know how I'd tell if there weren't.
For toothache specifically, we'd do a differential check: does the horse eagerly eat a soft mash, but won't eat hard cubes? If so, time to grab that tongue and do a visual inspection (and if everything looks normal, it's still worth palpating).
(a typical vet complaint is that owners don't do any of the above, and first notice only when stench ultimately makes it obvious to check for toothache)
And in your strange example, if this dog wasn't eating due to a toothache, the parents are forcing the dog to anxiously eat through the pain of a toothache.