Should I protect a patient at the expense of an innocent stranger?

You have categorized this question as referring to the case New York Time Co. v. United States. The issue at stake in the landmark case of New York Time Co. v. United States is whether the United States government may prevent a newspaper from publishing information that would put national security at risk. This has nothing to do with patient confidentiality. Thus, I think you may have intended to associate the question with the following New York Times column (printed as "The Ethicist"), which bears the title of your question, "Should I protect a patient at the expense of an innocent stranger?" (see attached link to article).
In this column, a physician writes in asking for advice. He discloses that he had previously seen a patient who suffered from headaches and whose headaches only cleared up after he had confessed to the physician that he had committed a serious crime. He then allowed someone else to take the blame for it. The hospital lawyer affirmed to the physician that he was not obligated to report the incident since the patient was not in danger of hurting others or himself, yet the physician feels guilt that an innocent man is out there suffering because of what his patient did and feels that he may be violating the Hippocratic Oath to "do no harm." 
Chuck Klosterman, the columnist, writes back that the Hippocratic Oath, while "good," does not deal with the modern problem at hand and, as a result, must be separated from the discussion. Klosterman identifies the root of the issue as the fact that the physician had promised his patient confidentiality, stating that the deeper question is "whether breaking this commitment is ethically worse than allowing someone to go to jail for no valid reason." 
Klosterman goes on to advise the physician to call the patient back to his office, urge him to confess to the proper channels, and, if he refuses, tell him that promising confidentiality was an error that does not override the need for social justice. Klosterman states, "You should not have made the original promise, and you should not allow that bad promise to stand." In other words, he is clearly arguing that a patient should not be protected at the expense of an innocent stranger. 
https://www.nytimes.com/2013/05/12/magazine/should-i-protect-a-patient-at-the-expense-of-an-innocent-stranger.html