As with most deals with humans it was a bait and switch as well, and indeed possibly historical revisionism -- if nothing else peanut butter would not have been known as it is a new world plant and earliest domestication of those is some 7000 years where dogs have been doing for some 23000.
The likely accepted path is
Some wolf dies (possibly killed) with cubs, cubs get taken. Possibly also some mutant that thinks humans are cool (just like some humans have a parasite that makes them think cats are cool)
Whatever cubs grow up to be less aggressive to humans, and possibly featuring said mutant trait, get to be the ones that breed, the others get killed or maybe just neutered.
Repeat for 1000 generations, possibly kidnapping other wolf cubs from the wild throughout this (to say nothing of being trained to hunt their wild counterparts to extinction or near enough). Likely also multiple parallel strands as well but DNA evidence for that gets a bit harder.
Now we are in ancient human times. What happened in more modern times still...