I was getting to know a guy a while ago (we'd discussed dating - he lived a few hours away so I hadn't met him yet) who had a woman friend (a past girlfriend) who he hung out with a lot. He'd been going over there every night to hang out with a group of others, staying until 1-2am. One night he stayed after everyone else had gone home, and talked with her alone until 7am. Again, he stressed that they were just close friends. It was no biggie to me because I wasn't emotionally invested in him, but if I had been, this would have been a red flag for me. If you are close enough to spend literally ALL NIGHT alone talking, then maybe that's the person you should be dating. I dunno.
I think that in a relationship, there will come a point when each person needs to put some distance between themselves and close friends of the opposite gender. It doesn't sound like the OP had come to that point yet, so this woman clearly over-reacted in a serious way. (Red flag there, maybe.) But boundaries are good, and necessary for a healthy relationship when the time comes. That isn't jealousy or possessiveness... it's just caution.