Welcome to the forum, I am so very sorry that you are having such a hard time understanding the frustration and pain your daughter is having. I also feel for her too and am so very pleased that you have responded in a way of love and support and that you have arranged some counselling for her, that is wonderful.
I am no professional just a person that cares so this is just my feeling, it sounds like she is experiencing some sort of "mixed emotions" and that she has used you to lash out her feelings that she may have had bottled up for a long time. Perhaps something did happen on the night out that has triggered her or made her realize she needs to speak to someone, as you mentioned, none of us are perfect parents,but if when you were hearing this you genuinely felt shocked then I think perhaps she has some things inside she needs to address.
Mental health is a really funny old thing, it can impact anyone. The fact she has always presented as happy and that everything is fine, is not really an indication that everything is fine. Perhaps on her placement she has felt like this path isn't for her, even though she had a great time(?) and got some wonderful feedback, maybe she feels scared that "what will she do now?". You mentioned she also stresses easily, this perhaps is another indicator that the words may not have been truths but she is letting her frustrations and pains out.
She does trust you and that she has come to you to say she needs to see a counsellor. I know it must hurt and must hard to hear that your child does not want to speak to you but to someone else but please try not to take offense to this. Have you asked her if she would like to see a GP?
I can hear how hurt you are and I am so sorry that you had that tirade of abuse thrown at you, you certainly didn't deserve that but I am so very happy that even when you are feeling so worried and scared that you have put her needs first.
You could also offer her to call the Beyond Blue Line to chat if you think she might need to talk to someone sooner, 1300 22 4636, or even for you to get some extra support through this time. There are some wonderful people on the other end to help you all through this time.
Seeing she is only 21 she can still call the Kids Helpline on 1800 55 1800 as they deal specifically with young people up to the age of 25 and are just amazing.
Huge hugs to you HLF, and I am not sure if I have been helpful but hope to chat some more.