Wow, there are lots of different opinions on this topic, and its such an emotional topic for parents too... I think the main thing you need to ask yourself, in order to make your decision, is WHY do you need her to sleep in her crib for nap-time, and WHY do you need her to go to sleep on her own? The main reason we try to get our son to fall asleep on his own, is because he WILL NOT sleep through the night, and apparently that might be one major part of the puzzle - if he's falling asleep himself, he can learn to fall back asleep himself during the night. IF your daughter is already sleeping really well through the night, then surely the main objective is to get her to sleep during the day somehow, and it won't matter if she does it in your bed, on the floor, or wherever. It sounds to me like she's learned that you will leave her in her crib, and will not respond to her during the day, so she is panicked each time you put her there during the day. If I were her, I'd work myself up to a frenzy each time as well! If I were you, I'd seriously look at your reasons for this, and look at just adapting a bit to her. There are some battles you will really need to win, like getting her to sleep on her own at night or keeping her safe. But, why make something like this into a huge battle, when it doesn't seem to be working, and there are lots of other options which might be more pleasant for both of you, yet also can help to accomplish your goal of getting something done in the day while she sleeps!
If you are really hoping to get her into her crib, why not do it in stages? Firstly, get her into a loose routine, by getting her to fall asleep in her chosen methon - i.e. nursing in bed with you - for a week or so. THink about really making it a routine - tell her we're going upstairs for a story, a nurse and a sleep. Make it pleasant, lovely, relaxed, and nice if you can. Don't expect to get loads done at first, in case she doesn't sleep for very long straight away. Try to have faith that over time, the more relaxed she gets about this, and the more used to it she gets, the longer she will sleep at a stretch. Tell her all about how you are changing your mind about how you are approaching this, but that she really needs to have a little sleep during the day because you can see how tired she is etc., etc. You don't have to worry about her understanding all that you say - she will get the jist of the respect you have for her, and the fact that you don't want to make this traumatic. Then, when she's used to that sort of routine, you can vary it in order to move her towards sleeping in her crib. Do exactlly the same routine - story, and then nurse, but just do that a bit earlier than you usually would, so that she doesn't actually fall asleep on the breast - then, put her on the bed with you to fall asleep on her own. When she's happy doing that, just move it to the crib, and sit next to her in a chair or on the floor etc, and do exactly the same thing that you did on the bed. You'll still probably find that she grumbles a bit, but it will be a grumble, rather than hysteria, at least hopefully - if she's over her fear of the crib by then... which, is potentially another issue, and which you may need to address separately, by putting her in there a bit when she's not tired etc. The baby whisperer book has some good ideas about getting them over a fear of the crib...
CIO never worked just straight out for my son - but, what did work, was what I described above - getting him into a rhythm with falling asleep at regular times by letting him fall asleep his preferred way - i.e. nursing - and then getting him to go to sleep himself later. I put him to sleep on my bed, because he was comfortable there, and just nursed him to sleep. He would at least take nice naps, and got into a routine that way. Then, I transitioned him slowly.
I hope that helps, and good luck. Please do let us know what you decide to do in the end, and how it works. There's no right way, but you need to feel really comfortable with whatever you choose. Don't let the books dictate your method, let them inform it, but choose what deep down you feel is right in your heart, and then you will see the most results.
I feel for you!
A.