Problem With Friend-Zoning

this might throw y'all for a loop: male, college student, and I'm the one doing the friend-zoning.

story: about two months ago, I met this girl, K, in an optional review for a midterm. we hit it off pretty well, and started talking to her almost every day. I can very well just be friends with a girl, but her body language obviously said otherwise. so, after about two weeks of talking, I asked her out, a bit awkwardly, I'll admit, but it worked well enough. she rejected me; not a "ask me in a week when I'm in a better mood" rejection, just flat out "no, I don't want to go out with you". okay, fair enough. I asked her if she was certain, because I don't ask twice. she was certain, and now we're just friends.

I spoke to one of our classmates, her friend, today. the relevant part of the conversation went like this:

Friend: so, when are you going to ask K out? she talks about you all the time. she really likes you.

Me: what? that doesn't make any sense.

Friend: K wants you to ask her on a date! ohh.. you don't like her do you?

Me: I already asked her on a date... that was about a month ago. she said "no".

Friend: ... ask again?

Me: I made it very clear at the time that I would not ask her again.

Friend: (spiel about how I'm being too harsh and careless and should just ask her out because [insert randomness here]).

so, RA, am I really being too unsympathetic? should I just ask her out? I'm not seeing anyone else, and she is very attractive and nice. on the other hand, god damn, does no one listen? being friends with someone only in hopes that maybe I'll date\sex them sounds retarded, desperate, and rather condescending to both parties.