This is more or less one of the central tenets of scientific study....you can't prove anything, you can only disprove things.
...except for beliefs. I have a group of old friends who are stident anti-GMO. Monsanto is the devil to these people, one of which probably won't talk to me anymore because I had a spray bottle of roundup in my garage.
It's proving a negative assertion, which is impossible. The burden of proof is on the person making positive claims.