The Answer:

This is not true. Although no president thus far has been born in DC, people born there are certainly citizens.

Here are the criteria for the presidency, from Article II, Section 1 of the U.S. Constitution:

No person except a natural born citizen, or a citizen of the United States, at the time of the adoption of this Constitution, shall be eligible to the office of President; neither shall any person be eligible to that office who shall not have attained to the age of thirty-five years, and been fourteen years a resident within the United States.

—The Fact Monster