I found a shop foreman before I left work. This is what we've got...

There are two types of fans on these cars.



The older fan is on top. It was replaced by the new style shown on the bottom.
The fans are indeed controlled by pulse width modulation. Essentially, the computer sends pulses to the controller kinda like a strobe light. If it flashes slow, the fan runs on low speed. If it flashes fast, the fan runs on high speed.
The computer sends that signal to the little metal box on the fan. That box reads the signals and turns on the low speed or high speed on the fan. When that box fails, the fan won't work.
The fan motor is seldom harmed when that happens. The smoke leaks out of the control box, not the motor. Four large wires come out of that box. You can bypass the box and wire straight to the leads. The fan will blow on the speed you've set.
The new style fans have the speed control built into the motor. When they get a constant 12 volt signal they default to high speed. That is a fail-safe that prevents the engine from overheating.

Apparently, the aftermarket fans are made cheaply and don't have the fail-safe logic built in. Should you have one that fails, bypass the metal box and wire directly. The fan will run just fine.

Since the majority of fans I have played with were the new style, I had no idea there would be a problem.

Apparently, all the smoke leaked out of your fan. You can contact the company and see if they will warranty the fan. Since they have that statement in the paperwork, they must know it's an issue. If they refuse to warranty the fan or if you simply don't want to mess with all that again, bypass the box and wire up the fan. I'm not sure which leads will provide which speed. I will play with my donor and see what I can find out.