"It’s important to note that merely bringing two masses of Uranium or Plutonium together that combined will make a critical mass will almost certainly NOT explode and ‘irradiate half of Chicago’. IIRC it IS possible that merely having a critical mass will explode but unlikely which is why nuclear weapons contain a neutron source to kick things into gear (by shooting neutrons into the mass they cause many more atoms to fission quickly thus engaging the dreaded/sought for chain reaction)."
A minor nitpick - nuclear weapons contain a neutron source because they create a very short lived supercritical mass by imploding the nuclear material with conventional explosives. It is necessary to have neutrons present to trigger the chain reaction in mid-implosion. If you could assemble a highly supercritical mass just by piling up bricks of uranium (you can’t) it WOULD go off on its own, triggered by spontaneous fission.
Strictly speaking, an exact critical mass won’t give a runaway chain reaction at all. On average, neutrons are lost at exactly the same rate as they are created by fission. For proper neutron multiplication, you need a highly supercritical mass, say, three critical masses for a bomb.
“Tickling the dragons tail” by moving two pieces of uranium together will create a barely supercritical mass. They don’t actually have to be touching - just close enough that sufficient neutrons from one are hitting the other. When you get them that close, spontaneous fission will start a runaway chain reaction and a lethal neutron flux. This is called a “blue flash” incident, because the neutrons streaming through your eyeballs emit blue Cerenkov radiation right inside your eye.
What you DON’T get is a nuclear explosion, at least, not a very big one. The uranium pieces heat up very rapidly and expand, becoming subcritical again due to their reduced density and increased surface area. This is a good time to pull them further apart, since you’re walking dead anyway and they’ll become critical again as they cool down. You’ll burn your hands, but you deserve it!
If you’re being really reckless and clap those pieces of uranium together as fast as you can, you might get a bang. As soon as they are close enough to be supercritical, they start to heat up but they’re still moving towards each other. However, they will release energy fast enough to blow each other apart long before a big supercriticality is achieved. The yield of your nuclear “explosion” is likely to be slightly less than a firecracker. (Although you’re still walking dead from the neutron flash.)
To get them together fast enough to take out Hiroshima, you need to fire one piece at the other with a gun. That is literally what was inside Little Boy, a gun barrel with a uranium shell and uranium target. (There was a neutron generator as well, but it wasn’t strictly necessary.)
With plutonium, not even gun assembly is fast enough to achieve a large supercriticality. That’s why implosion and neutron generators are required, which are thankfully technically difficult to construct!
So the story could be true, but the worst case scenario is an irradiated lab rather than a mushroom cloud.