I'm seeing some technical, practical, and political reasons to think a low yield nuclear test did not occur.
The radiation lab results do not directly support it. Fission products include significant gamma in addition to beta. And alpha should be present, too. The lab only detected beta.
This itself isn't definitive proof. The report does not say how alpha and gamma were ruled out. The STS-6 Geiger tubes used for quantifying beta contamination on the clothing are completely insensitive to alpha. So that means the lab must have had some other type of detector that was alpha sensitive, but the report didn't name it. I don't know whether the lab likewise had a very sensitive gamma detector (like a scintillator) or not. This is important to know; it would give us a better idea of whether we can rule out a fission explosion, or if it is possible that the clothing did contain fission fallout that was above the detection threshold for beta but below the detection threshold for alpha and gamma.
Still, this is why I'm suggesting the incident was caused by conventional explosives spiked with Sr-90. It would explain the contamination without us needing to make any assumptions about the lab's equipment. A fission device could only be possible if the lab missed the gamma.
But the bigger reason I don't think a nuclear test was responsible for the incident was that the USSR had a moratorium on nuclear testing from November 1958 to September 1961. See https://en.wikipedia.org/wiki/Partial_Nuclear_Test_Ban_Treaty
for more background.
Khrushchev had been lobbying since 1955 for a test ban. This makes a whole lot of sense from his perspective. The USSR's economy was weaker the US's, which would make matching the US's R&D efforts relatively more costly. One could view the USSR's ultimate collapse as stemming from the economic strain of the nuclear arms race and space race with the US, which supports the necessity of a test ban from a Soviet perspective. And it would have kept France and China from getting the bomb.
Eisenhower initially wasn't interested. There was concern that the Soviets would cheat. But an interesting point is that the US believed atmospheric tests as low as 1 kT could be detected reliably; one of the big technical sticking points was whether detecting underground tests reliably was possible.
Khruschev finally got what he wanted in November 1958, with the US, UK, and USSR agreeing to a voluntary testing moratorium. Had the moratorium held, I think we'd be in a very different place. For starters, I don't believe miniaturization of H-bombs was completed by then, so ICBMs with MIRVs would not have been possible.
I cannot see Khruschev taking the risk of cheating just 3 months into the moratorium, especially with something as easily detected as an atmospheric test. The stakes were too high. I believe getting caught cheating would have closed the door on future international cooperation around nuclear test bans.
Plenty of people in the US weren't happy with the test ban, either. I'm sure the US was watching the USSR for any violation that would enable the US to resume testing. And the US didn't catch any cheating, in spite of the motive, at least up until the USSR withdrew.
The USSR was doing the bulk of their nuclear testing in Kazakhstan and in the Barents Sea. Nuclear testing is not simple. It takes a lot of equipment and personnel. On one hand, if the USSR wanted to cheat, they probably would need to do so in an area different from these. But that would require relocating and setting up a lot of new infrastructure. And the military would need a lot of build up in the area to make sure the test area really is evacuated; having witnesses to it could lead to an international scandal. As was mentioned in a different thread, the area had indigenous people and other tourists, so I don't see it as a good place to do a test where absolute secrecy is essential. Meanwhile, such a military presence, plus setting up the testing infrastructure, likely would draw attention, which increases the risk of discovery.
Also, testing is typically done as part of a series. A test of a single very low yield device isn't going to produce much valuable information. And trying to pull off a series of such tests is going to increase the risk of getting caught.
I just think the risk vs. reward ratio is far too high for Khruschev to cheat by attempting a nuclear test in the Urals. The US never detected any cheating. And fission contamination would be possible only if the lab missed detecting the gamma that would have been present. Overall, it seems too unlikely.
Ultimately, the moratorium fell apart. France began conducting nuclear tests in February 1960. The Berlin Crisis happened between June and November of 1961. The USSR pulled out of the testing moratorium in September of 1961. This also enabled them to test the Tsar Bomba, the largest thermonuclear bomb with a yield of 50 MT, in October 1961. The Cuban Missile Crisis occurred in October 1962. In October 1963, the Partial Nuclear Test Ban Treaty went into effect, which mandated that all nuclear testing occur underground. The Threshold Test Ban Treaty was signed in 1974, which limited underground testing to 150 kT. Ultimately, the Soviet Union fell before the US finally stopped nuclear testing in 1992 as part of negotiations for the Comprehensive Nuclear Test Ban Treaty. Of note, the US has not ratified this treaty and it has not formally entered into force, so nothing is stopping the US from resuming nuclear tests.