I've worked in quality control in another industry (brewing) as a process physical chemist. There is always going to a a conflict of interest when you test internally, and the results aren't what the management want to see. However, there are ways to mitigate this.
You can split the tests into three main categories: cosmetic, financial and safety, with different allowed variances for each.
As a financial example, we had to pay excise duty on the alcohol, so the tests for ABV were stringent and cross-checked by reference laboratories. All internal tests were done with robust internal controls using gas chromatography and every few months, a random set of samples would be cross-checked with a reference laboratory by distillation. The internal results could be trusted because they were routinely validated, and the instrumentation calibration was checked for every single run.
When it came to safety, this was also taken seriously. Two incidents I recall were a hoax call from someone claiming they had contaminated the water supply with paraquat (weedkiller) and another where some stainless steel tanks had developed microfractures which caused coolant (high concentration KCl) to leach into the product. In both cases all the stops were pulled out to collect samples and get them checked by a reference laboratory. No one wants the bad publicity or being sued because the product was contaminated with something nasty.
Things were a bit laxer for cosmetic checks (colour, taste, CO2 concentration etc.). However, there was a clear specification for each test detailing min/optimal/max for each metric, and it required management sign off to allow non-conforming batches to be passed through. They were usually blended with higher quality batches to bring it in line with the specification.
So overall, the point I want to make is that where there were legal or safety requirements, having regulations and financial penalties in place did cause the company to care very, very deeply about accurate testing, including having internal tests cross-checked by an independent external laboratory. And for every product defect, there was a chain of accountability via management sign-off, with the understanding that the QC department was independent and impartial. We used to rigourously check every single batch at every stage of production, including multiple replicates for critical tests, and also including the packaged end product. Reading the story about talc, this didn't happen on any appreciable scale. The question I have for talc is this: why didn't they do this level of testing, taking samples from each lorry load out of the mine, after processing and refinement, and after packaging? The testing might not have been as accurate as they might have liked, but they didn't even seem to try to get an impartial picture of the level of asbestos contamination, perhaps because they didn't really want to know, and instead stuck their heads in the sand and pretended the problem didn't really exist. That's what seems wilfully negligent here.
We also had an entire department which stored a few tens of bottles/cans/kegs of each batch, and we would test one of each every few months to check changes throughout and beyond the nominal shelf-life. The story mentions testing a single package of talc from the company museum. The question here is, why didn't they have a library of stored packages from every batch ever made? This would have permitted re-analysis over time. It might have even reduced their liability since they could prove which batches were contaminated and which were not.