"Putting the science on trial" does not mean filing a court case against science.
Putting the science on trial means appealing the ruling and ripping the science to shreds in a venue where the transcripts are often made public. How in the world do you have an opportunity to prove that you are not guilty and chose to not do it because you don't like the arbitrator. Its just your circular, flawed logic.
Whether Davis won or lost is not relevant to your claim that owners cannot sue the league. He sued. They didn't reject his case based on your belief that he is not allowed to sue, they didn't put him in jail, they didn't take his team away.
Whether you can sue is as apples to apples as it gets.