I don't know why you think there would even be a question as to whether or not it was rape. It clearly was. And keep in mind that a butt-load of men have been convicted of rape without DNA evidence. She could still pursue a charge if she wanted to. I always encourage people who have been raped or sexually abused to pursue it legally, but at the same time you have to respect their decision if they decide not to.
I would also caution you against confusing the roles between a friend and a counselor. You don't have the right to "make her" talk to you about it, particularly in detail. That kind of think is usually best left to a professional. When a person starts reliving that kind of trauma, there is always a danger of what we call "retraumatization". That means the person can experience the kind of emotional, and even physical, reaction as if it were just happening. That's why it's normally a good idea for talking in detail to be done in the safe zone of a trained professional. Not all the time, but most of the time. I also have problems with making a person feel like they have to tell their traumatic story over and over again. First of all, a person should always be in control of who they tell and when they tell. A person who has been raped typically feels a total lack of control. They were forced to do something huge against their will. So one of the core elements of treatment is to help them feel they are gaining that control back. One of the important ways this is done is by helping them have control over their story. That means not forcing her to tell it when she doesn't want to tell it, or to someone she doesn't want to tell it to. That might be swallowing your pride and dealing with the fact that she doesn't want to tell you. That can be hard to take. You might see that as a statement on your value to her or your trustworthiness, but that's not necessarily the case. Maybe she's protecting you from her story. Or maybe she values your friendship so much that she needs you for comfort and support. And don't overlook that fact that her telling you the story in detail might actually have a negative impact on your friendship. We also have to check our motivations for wanting to hear the story - even us "trained professionals". Do want them to tell it for their own good, or is it to satisfy our curiosity? Or maybe even because we feel like, if they tell us, that means we are valuable to them.
You obviously care about your friend and want to do the right thing. I would say encourage her to continue working with her Therapist/Counselor. And maybe you could find a professional to talk to who can help you figure out how to best help your friend.
Screw the whales, save the subjunctive!