I am a nuclear engineer. I have designed critical systems, run a nuclear reactor, and have personal experience with radiation.
As such, I do have the training to examine the claims about prompt supercritical effects and power levels.

The claim that a small bare sphere of plutonium would have certain effects, and is supported with anecdotal evidence of the Godiva and Demon cores (one just critical when bare and cold, the other subcritical when unreflected). Jezebel was in operation at LANL until very recently, I could find people who worked with it easily enough.

And how can you make claims about archival footage; do you have access to top secret clearance and the Argonne video library?

Now, there is some evidence that the nuclear data sets for fissile elements might be manipulated to make bomb design dangerous with the public data. Pu239 and Pu241 are rare enough that it would be possible; and the non-compliant countries such as Pakistan and India are not known for their clarity about their nuclear data.

As for the difficulty of getting plutonium: its bunkum. the reason the UN has to have a complex system monitoring the entire world is to prevent the very easy creation of plutonium from a natural uranium and carbon pile. It is the job of a few months to get enough plutonium, and the work of a month or so to do the chemical separation.