Principled values show their strength when they are tested. This is the case in “The Drumhead”, as an admiral comes onboard to investigate a possible sabotage on the Enterprise and a potential larger threat to the Federation. There was, indeed, an incident, and an implicated spy onboard. This concluded rather quickly, leaving us to realize there was more at stake.
What begins to unfold resembles a witch hunt. It is true that there is an Enterprise crewman who has his hidden his true identity, he is part Romulan, an enemy of Cold War mentality. Crewman Tarsus lied and forged his documents to enter Starfleet, knowing his heritage would disqualify him from serving. And he did, by coincidence, get wrapped up in the actual conspiracy that occurred on the Enterprise.
But the admiral-investigator does not relent. Her and her team continue to interrogate Crewman Tarsus, making him an example of the larger, faceless threat that the Federation faces.
Only Picard defends Tarsus. Picard is reasoned enough to admit that Tarsus has done wrong by concealing his identity, but that alone does not implicate him in this broader conspiracy. Picard’s defense likewise becomes subject to critique and suspicion. By aligning himself with Tarsus for a fair trial, Picard’s entire reputation, in front of his entire crew, is questioned and on the line. This does not deter Picard. If his career is tarnished, he will go down with his principles forming his decisions and his integrity intact.
Picard is a statesman. Yet he pressed against wrongdoing done by his organization, he will stand against it, with the odds stacked against him. He does something similar when defending the Baku race in Star Trek: Insurrection. His integrity is unshakeable, even when against orders from higher-ups that have turned sideways. He is the Picard.