I'm not sure if a wild animal has ever been observed to have a pet, but I guess many intelligent animals value playfulness and companionship, and have evolved to have tolerance and empathy, so judging by Twitter, etc, it doesn't seem that rare to have inter-species friendships even between animals that might be considered as predator and potential prey.
You don't just rock up to a herd of wild bovines and say "hey, you're my cows now, let me milk you". Rather, one day a group of humans started following a herd around, killing one once in a while for meat; eventually perhaps they started protecting the cattle from other predators and guiding where the herd went, while also starting to find ways to continue lactation in females and get them to acquiesce to being milked.
The cows that were compliant to the slow changes were the most likely to reproduce; rinse and repeat until you get whatever we have now.
There's no peer-reviewed scientific research describing this phenomena. Or even any attempt at gathering any data with something resembling scientific rigor.
A simpler explanation is that these dogs and baboons are just... Living side-by-side in a garbage dump. And that the film-makers just didn't include any footage that didn't fit their narrative.
That said, on a personal scale:
My pets have definitely changed me and made me better.
"Then as now, this was a good deal for the humans too. The scavenging dogs weren't just a sanitation squad, they were also security." [1]
Watching a collie herding dog in action, or I presume a hunting dog, is quite amazing. Hard to believe humans wouldn't have watched and learned.
Also that 14,000 year domestication date mentioned in the article sounds remarkably similar to the dates humans began the processing of "domesticating" (settling) themselves, and is basically the marker for the end of the last ice age, too. Keeping crops and herds of animals and building permanent villages to guard and control definitely benefits from having canines (and felines for pest control, too).
We know by now how we turned the grey wolf into the dog, but do we know what the relationship has done for us? What have wolves taught humans?
Some hypotheses to get you started: they might've taught us the power of collaboration. The power of social hierarchy. The empathy towards other life forms. Anthropomorphism (maybe that's why we have furries today). I don't know, but I very much doubt the domestication of wolves has been a one way endeavour.