... Basically the theory is that the Soviet nuclear assets where verging on "spontaneous" self destruction due to inferior design techniques and the world needed the cold war to end so that the USA could secretly get inside the soviet nuclear system and help restore it's security and integrity (with Soviet permission). ...
I don't thinks that is correct. Both the US and the USSR, chose less safe alternative reactor designs to facilitate the construction of nuclear weapons.
Oak Ridge had made a prototype of a Thorium Reactor, and ran it for a year or so, but it is a very poor path to generation of plutonium, that could make A-bombs. So the funding for that research was cut and greater funding built a gaseous diffusion plant to enrich the U235 content. It was located where the government owned TVA hydroelectric power could drive the pressure pumps. (That part of Tennessee had low population then, and there was lots of excess generation capacity and transmission grids were not yet able to move all the generation capacity to where it could be used. - I.e. the power for the pumps was essentially "free." Centrifuge enrichment was not as attractive then - more technology development needed to make it the better choice as it is today.)
The USSR, did not have the TVA's "free power" so chose a reactor designed to maximize the production of Plutonium. Unfortunately for all, that type reactor has a positive temperature coefficient. I. e. the hotter the core, the faster the reaction rate, but they can be safe with control rods. The temperature coefficient, its value, was known only from theory. So probably with some vague permission from higher ups, at least locally the decision was to measure it. This was done late (past midnight, I think) when Chernobyl's power was not needed and the reactor could be taken off line. Also some of the safety controls/over rides had to be disabled, even with the control rods partially withdrawn.
There are some details I forget fully but the tip ends of the control rods actually increase the reaction rate and that complicated the planned measurements. Not sure, but think some rods were left fully inserted while others were essentially fully removed for the test.* After the core temperature had risen (and the reaction rate) and measurements of both were reasonably accurately known, they started to re insert the with drawn control rods, but they (or some) would not go all the way down. With their tips in the reactor boosting the reaction rate along with the higher temperature, and no way to slow that reaction rate increase down, some one said, (in Russian): "Lets get the hell out of here." and the rest is history.
* I suspect that also contributed to the disaster. I. e. parts of the reactor core near these fully inserted rods were cooler than parts with their local control rods withdrawn. I think this thermal gradient could easily warp some of the fuel cases, bend them slightly even. As Murphy noted: "If anything can go wrong, it will."
I think any "help" was with the command & control of the weapons, not with the weapons and "went both ways." I. e. as part of their mutual interest in making sure now crazy general started WWIII, both sides reviewed the C&C systems of the other to both see if theirs could be improved and most importantly to be assured the system was safe from some nut who wanted to commit suicide with all regretting his death.
I would also like to note, that their is a strong and dangerous POV that the US has the best technology, and others like USSR or now China must steal it. I worked at LASL, two summers, helping to make a high temperature vacuum furnace.* (My tasks focused on some water cooled probes we could insert into it.. Parts of them and the main, electrically heated cylindrical chamber were of necessity made of titanium.) LASL was one of only 2 or 3 places in the US that had the techology required for fabrication of titanium parts then, but the USSR was already making the leading edges of their super-sonic jets out of titanium. I think this is why some Migs (lent to China, I assume) could cross the Yaula River (China's border with N. Korea) fly south, fire the ordnance in support of the advancing N. Korean hoards, and quickly turn tail and out run anything the US had at the time safely back across the Yaula.
* Cesium has the interesting (and unique, I think) characteristic that when molecule collides with very hot metal, it leaves as an ion - having given an electron to the metal. Idea behind this program was to some day install these "thermally energized" electrical units inside a heat source (nuclear reactor ?) - To hell with that steam turbine, etc. - make electric power directly from thermal energy. Unfortunately, AFAIK, the death of the sole full time researcher, Neal C., ended the investigation. My VW blew its timing gear on the drive west for the second summer, so I arrived after a weekend. On that week end, Neal and one other were leading a party of "Rock climbers" in Colorado and both were buried exploring an alternate path's rock slide - bodies never recovered. I had learned from Neal the summer before the basics of rock climbing. My broken VW surely saved my life. Only knowing Neal, I would have gone with him. Only I knew any details about the vacuum furnace. - My 2nd summer job became to assemble it as best I could and write a manual on it. I doubt Neal's idea has been investigated more.
The three "faits" were cruel to Neal, perhaps to the entire world if Neal's idea was great, but kind to me - broke a timing gear deep inside my VW's motor.
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