"Independent" just means no direct connection on the face of the relationship between team and doctor. Off-the-record communication is still open game and these teams have the resources to bend the rules.
Two, you can pass all of the tests but perhaps still suffer symptoms that do not get captured by the test. You can get scans, you can ask questions, but they can't ascertain everything. This applies to general results like blood work. You might just fine in your 30s eating junk food and the bad results don't become visible until 50+ years.