In this era of figure-skating and other sports-judging scandals, is it possible that a judge might intentionally give an outstanding same-country contestant an average or poor score just to show that he/she is not biased? (Assuming the judging isn’t anonymous - for instance, an Italian judge - on a panel of many judges from many different nations - deliberately giving an Italian skater an average or poor score).
Are you asking whether human nature would make this possible? Of course. It can even happen unintentionally. Are you looking for examples? I don’t know if any on hand.
The Italian judge would also plant a bloody knife in the American skater’s locker 
There’s also the possibility of a judge giving the #2 or #3 athlete from the same country a lower score as “proof” that his high score for the #1 athlete from that country wasn’t necessarily out of national bias.
However, national bias could also be explained by cultural bias. In the 2002 Olympic pairs figure skating scandal, the four judges besides France who voted the Russian pair ahead of the Canadian one were from countries (Russia, China, Poland, Ukraine) where the Russian “traditional style” predominated.
The Olympics throws out the highest and the lowest scores just for this reason.
Don Cherry, the man whom Canadians named as their 7th greatest Canadian ever, complains about Canadian judges doing this on his radio show “Grapeline” with Brian Williams (no, not that Brian Williams).
Keep in mind that, through 2002, figure skating did not do this - in fact, the scores themselves were not comparable between judges. Instead, each judge’s scores were used to rank the skaters (i.e. Judge 1 had a ranking of the skaters, Judge 2 had a separate ranking, and so on), and the rankings were then compared to each other to determine the result.
The first fight between American Evander Holyfield and United Kingdomite Lennox Lewis resulted in a controversial draw. Virtually all observers saw the fight as a clear victory for Lewis. One American judge scored Holyfield as the winner, not much of a surprise there, however the British judge scored it a draw and many surmised as a polite Englishman he had given Holyfield too much credit in order to avoid appearing to be biased. This was a major failure on that count, plus apparently he didn’t know that national bias is an integral aspect of scoring boxing matches.
Not if he wants to keep judging.