Can you give us an example? .
That's easy - look at last year's worlds. No American judge. Take out the Russian judge and replace him with an American judge. Do you really think Domnina/Shabalin would have won gold with that mistake filled performance if there was no Russian judge on the panel? Do you really think an American judge would have placed them first?
[and I also agree that Davis/White might have got the bronze if an American judge was there]. Judges have a big influence on results.