Most close friends and my sister know my passwords for everything (i have the same passwords for most things) but i trust them and see no reason why they shouldn't know them, they even know my bank pin number and i know all of theirs! (do u think we're too close lol)
Anyway, it's totally up to you and i think that your friend was wrong to be funny with you because you wouldn't give it her! even though i don't mind, if one of my friends didn't want to give me theirs for whatever reason i would totally understand.
If this situation comes up again, just tell her you will type in the password for her if she likes, surely she wont have a problem with that?