The hypothesis under test was something like "expression of tameness is genetically linked to expression of physical characteristics, such as spotted fur and floppy ears". It's quite valid in that context: Belyayev started with a population with a low (perhaps non-zero) level of domestication, ended with a moderately domesticated population, and observed the physical differences.
"The history of the Farm-Fox population undermines the commonly repeated narrative that a suite of domestication syndrome traits emerged solely as a result of selecting on tameness. There is no temporal link between most of the syndrome traits, which first appeared in Prince Edward Island (PEI) fur farms, and the later behavioral selection in Russia."
On the spotted fur [1]:
"The farm-fox breeders of PEI intentionally selected for white spotting and other unusual coat patterns (Figure 3). They noticed that crossing two white-marked foxes occasionally resulted in animals that held their heads askew, a phenomenon Belyaev would later describe in his population, suggesting shared genetic etiology. White spotting was more common in Belyaev’s selected than unselected populations, but has not been associated with less fearful behavior in individuals (Figure 2D)."
On the floppy ears [1]:
"The farm foxes of PEI occasionally had floppy ears, even as adults (Figure 3C). In the Farm-Fox Experiment, ‘delayed ear raising’ was noted (ears floppy past 3 weeks of age, but not necessarily into adulthood). While slightly more common in the selected population, the trait is extremely rare, and no association between delayed ear raising and less fearful behavior in individuals has been described (Figure 2D)."
"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...
"A widespread misconception maintains that the Farm-Fox Experiment started with wild foxes and recapitulated the entire process of domestication. Belyaev himself accurately described the founders as fur-farm foxes, but by referring to the unselected population as ‘wild controls’, contributed to this misconception. In reality, the experiment started with a fox population from eastern Canada that had been captive and purpose-bred since the late 1800s, something Belyaev and his colleagues may have been initially unaware of."
[1] http://dx.doi.org/10.1016/j.tree.2019.10.011