would you correct them?

Lately, work has been extremely busy.  Working in excess of 80 hrs/wk.  While the doubling of my paycheck is nice (though it's not time and a half), I'm absolutley exhausted.  It's beyond physical exhaustion, to the point of mental exhaustion, and making stupid mistakes.  My brain is just not functioning sometimes.

Case in point ...

Yesterday at church, I did the usual social butterfly thing that is necessary for the sake of building community.  Saw one person that I didn't know well, but I was convinced that I knew who she was.  I not only called her by name, but I introduced someone else to her.  Background and all.  There was nothing about the interaction to make me thing I was mistaken.

Later last night, it suddenly dawned on me that I mistook her for someone else.  That wasn't who I thought it was.  I did know her and I know who I mistook her for.  But obviously not well enough to prevent that mistake.

One of my more embarassing moments.  Not cuz I merely called her the wrong name, but because I kept going with it.  Introduced her to someone else.  Gave (the wrong) background info.

Needless to say, once I realized the blatant mistaken identity I asked on of my roommates for her phone number, left a message apologizing for that mistake.  Fortunately no one was hurt (I think), but it was extremely embarassing.

However, as I was dealing with my embarassment, a question came up ...

Why didn't she correct me?  It would have been much less embarassing if she had stopped me and corrected me.  While the shame is on me for making the mistake, she could have stopped the bleeding by correcting me.

So, balancing with my embarassment is my wondering, why didn't she correct me?  Would you correct someone in this situation?