Does the lab you don't trust also not trust themselves? Do they then pay another lab to independently verify your blood work? Do you then trust that them selecting and paying the 2nd lab didn't influence the results?
I agree that IF the plaintiffs dispute the results, they should be allowed to select AND pay for their own testing. If those results are different, then further investigation would be warranted. Something tells me the deceased's family is saying the results are irrelevant, because they know independent testing would likely confirm the ME's results and be a waste of money. Just because he was loved by his family, doesn't mean he was all the wonderful things they spoon fed the media.
My point is that 3rd party lab work is not cost prohibitive, but to your point, my company must test DOT licensed operators, we do not collect samples for testing or perform the tests ourselves, we also do not require the employee to perform the testing, we use a 3rd party lab.
The people absolutely should not trust government labs.