They began by talking to Boeing technical auditors that were sent to conduct an investigation at Ducommun. Boeing did an on-site inspection of this supplier because they the components they were receiving were "non-conforming" - wrong angles, shape, size, holes, whatever -- basically out of tolerance to the point they often wouldn't fit where they were supposed to be placed in the aircraft. These parts were expected to have been created with a precision CNC router - a device which typically does not have problems with tolerance unless it's broken or the operator isn't competent. Thus, auditors had reason to believe something was very wrong at Ducommun. The 737NG is only certified as airworthy if it's using those components created with the CNC process per the FAA approved design plan. These facts don't seem to be debated by anyone.
The plot thickens:
The auditors said they discovered that the supplier did not use a CNC machine to create the parts; rather they were being hand-made by crudely applying a template sketch on stock metal with a sharpie pen and then cutting and drilling to create the final product. Since all components Boeing had previously installed in their aircraft had certification that they were created from a CNC router the auditors realized that the supplier had been falsifying those reports. They said the supplier provided access to the true records confirming the deception. There doesn't seem to be much doubt that this was indeed the case; there are photographs and documents showing the parts were not created in the manner the supplier said they were. That evidence, combined with testimony, internal Boeing memos and the problems during assembly that prompted the investigation in the first place seem fairly convincing: Ducommun was using a "Rosie the Riveter" type of production method that created components with the same tolerances you'd find on WWII era vintage aircraft.
And now to your point that the program was speculative and had no proof of safety issues: I believe they did point to enough evidence that it seems reasonable to believe that many 737NGs are flying with Ducommun made components, and that those parts of the airframe are not airworthy (basically not certified for the weights and altitudes that the FAA has approved them for). It doesn't mean that they'll fall out the sky they moment they hit their flight ceiling or the first time the plane hits a bump, it only means that the actual strength and reliability of each airframe is completely unknown. Safe? Unsafe? Nobody can say.
Now the conspiracies theories:
If you're Boeing, you realize you have a multi-billion dollar liability on your hands that will bankrupt your company 10 times over if you actually had to tear apart and inspect or rebuild all the suspect aircraft. So, you bury the reports, fire anyone involved, call in all your favors and unleash your lawyers with all the political power you have as a major defense contractor to make it all go away. (The program suggested that's exactly what they were doing).
If you're the government, you realize that one of your biggest defense suppliers has a problem that could bankrupt them and jeopardize the delivery of multi-billion dollar aircraft and weapons programs -- as well as put hundreds of thousands of Americans out of work. You shake your head, call them idiots in a scathing private email to their CEO and then help them clear their name by closing all investigations and declining all further comment.
If you're an airline and you find out that all of your aircraft were built with suspect components, what can you do? Boeing won't give you all new planes, and you can't raise a stink about it to anyone without causing a mass panic and decimating public confidence in your airline. You accept the apology discount Boeing gives you on your next order, go home, have a huge glass of wine and hope nothing happens.
Boeing, like AIG, is "Too Big to Fail(tm)"