No, I didn't. So she didn't make it to one class; big deal. Penalize her in some other way if you want. Failing a student for missing one class, for any reason, is just being a dick. People have lives, you know. Would you rather her lie to you and say she has explosive diarrhea?
Let me ask you this. The purpose of the class is so that the student can learn something by the time the class is over. By missing one day, has she ruined her chances of ever learning anything? No. So get over it; your class isn't the absolute most important thing in the world.
That essay might be time sensitive and must be done NOW. You don't know what other crap she may have had to go through recently and simply does not have time to do both the essay and your class in one day. Your class isn't her only responsibility in life. Sometimes, judgement calls like this have to be made when shit hits the fan. She's an adult; don't treat her like some little whipping bitch just because she has other responsibilities and chose to be honest with you, rather than to lie.
Where do you teach? Would they fire you if you missed one day? Did you get bullied in school or something?