I took a contest entry written by Seth Brown of Williamstown, MA in 2003, and I converted it into this puzzle.
Disclaimer: Events described in this puzzle are fictional.
A White House stenographer transcribed the following conversation between Barack Obama and Benjamin Netanyahu.
Obama: Who is on first?
Obama: No, the guy playing first base.
Obama: You're the first baseman?
Netanyahu: No, I am asking you. Me?
Netanyahu: You mean that man right there?
Obama: He's on first?
Netanyahu: What do you mean? There aren't any females on the team.
Obama: Well then who's on first?
Assume that nobody on the team is named "Who", "Me", or "He". With that assumption, the conversation doesn't seem to make any sense. But it actually does make sense. Explain how.