there's a cognitive disconnect in that proposition

The disconnect is in the differences in the processes. Just because a natural process has been occurring for 15k years doesn't mean that a similar process, directed by intelligent intervention would take 15k years to complete. The Siberian fox farm breeding program was (is!) an experiment conducted under controlled circumstances, directed towards a specific goal, (tameness,) whereas natural evolutionary processes tend to take more rambling paths with many branches and dead ends.

Wolves probably began changing due to enjoying some benefit from living in proximity to humans. That happened a long, long time ago. Tame dogs probably appeared towards the beginning of the 12-15k year period you mention. Tame dogs haven't taken that long to evolve, thoguh the many breeds of dog we have today are more recent, intentional creations.

Evolutionary biologists do not generally work in time frames, but rather in generations. As the documentary mentioned, after 8-10 generations of (human, specific) selective breeding, there was a marked changes, physiologically, and in the group's behavior towards humans.

When humans intentionally breed to select for particular traits, remarkable things can occur in a small number of generations. Natural selection is a very different process that gradually unfolds over time periods differing by many orders of magnitude. The theory of punctuated equilibrium proposes that organisms don't change much for very, very long periods of time, and that evolution occurs in infrequent, rapid bursts.

In addition to the quantitative changes to the silver foxes' evolution, qualitative changes were observed as well, suggesting that human-directed breeding is not simply a acceleration of natural evolution. These are inherently dissimilar processes, and cannot be directly compared in terms of time-frame or results.

Depending on the reproductive cycle of an organism, a plant or animal can be radically, even fundamentally, altered in a very short time. If this weren't the case, the many types of breeders at work on many plant and animal species wouldn't have jobs.

tl;dr I'd let my child play with one of these foxes.