Melpomene was the nickname given to the female marathon runner at the 1896 Athens Olympics. She was met with derision and disbelief and, since her identity was uncertain and her achievement and presence were viewed as distasteful and pathetic by the noble gentlemen organising the event, was nicknamed after the muse of Tragedy. She is believed to have been Stamata Revithi, a poor local woman of no other noteworthy accomplishment and meriting no other mention in the annals, who was not trying to make a point but rather a buck (or drachma, as the case may be). Reports regarding this event aren't all consistent but most accounts say that she ran on the day following the one on which the men's event was held and may have run it once before, several weeks prior to the Olympics.
The organization of Greek participants in the Olympic Games, probably the most reliable source, mentions only that she ran but not on which day. Accounts that record two woman runners by the names of Melpomene and Stamata Revithi should be regarded as inaccurate; it is almost certain that they were one and the same person. There was no women's marathon until the 1984 Games.
As a side note, the stadium used for the 1896 Games is U-shaped, the open end of the U being the entrance, and virtually every spectator inside the stadium would have been able to witness an argument taking place at the gate since it's visible from practically anywhere in the stands. The stadium has excellent acoustics too. I think there would be many more witness accounts had it happened while there were events in progress. Ms. Leder may be right in her account of the events but I find it a bit more likely that her version is a romanticised one.