Yes, qualification testing is conducted by independent and accredited entities, because other organization oversee the testing. The agencies do an admirable job with their testing, and the agencies are accredited. Because they are accredited, they can be trusted to do an honest and competent job making sure that the testing is done fairly.
While some qualification testing may be conducted by independent and accredited entities, not all of it is because of the ability to do qualification testing under a confidential contract. Due to this fact, there could be problems with the testing if someone had an "in" with a particular company and orchestrated things to turn out in his/her favor.