"The Farm-Fox Experiment selected for a behavioral trait that already existed in the population (Figure 3), essentially recapitulating a selection experiment performed on numerous occasions with dog breeds. [...] The change in the critical period of socialization in the selected foxes is more like the difference between more and less easily socialized dog breeds than between dogs and wolves."
You can check for yourself how the foxes brought to the US behave on Youtube[1]!
Also, the similar study with mice[2] by the same Russian Institute seems to have had even more striking results.
The rebutal seems to be using only theoretical objections, without any new original, empirical findings, to counteract tangible evidence that had been accepted by (and astonished) numerous other researchers who actually came into contact with the animals.
[1] https://www.youtube.com/watch?v=4dwjS_eI-lQ [2] https://www.nytimes.com/2006/07/25/health/25rats.html
"Dr. Frank, among other things at Montreal, had a pair of tame foxes lead about on the main streets, driven around in automobiles and taken to a public dance, where the girls did the fox trot with these foxes around their necks, and all this was photographed, moving pictures taken, etc., and to cap the climax Dr. Frank hired two airplanes, took up a pair of foxes in one and from the other airplane a photograph ground out several reels to be shown in the movies in the near future."
How common these traits were is another difficult question. But given that there was prior selection for tameness and that Belyaev specifically looked for those tame foxes to include in his experiment [3], it does not seem so surprising that this trait very quickly became more common.
[1] https://www.washingtonpost.com/science/2019/12/03/tame-foxes...
[2] https://babel.hathitrust.org/cgi/pt?id=nyp.33433090788674&vi...