In general, no, they aren't "embarrassed" by the situation. That's an inaccurate and rather dismissive description of the situation.
As much as I don't like disagreeing with you, I'm going to have to here. Yes, embarrassment is often one of the first things that comes up in these situations. I'm not saying it should or that it has any factual reason to, but yes, it does. "What did I do wrong" or self blame is one of the first things that often happens, along with being just embarrassed that the whole thing even happened.
This is a horrible situation, but in experiences that I've had with people (literally one at Gen Con) and as an RA, getting past that point is a huge issue. I've been at the ER with friends in this situation who were amazingly strong people who could kick my butt, and this was one of the things they had to deal with. Later on, it was one of the things they recognized as being absolutely wrong-headed, especially after some counseling.
Embarrassment is one of the key barriers that keep many people from getting help in situations ranging from assault to abuse to mental health issues.
I'm in no way trying to minimize what happened here: the memories I have of helping friends deal with that issue are some of the most intense from my college years. You might think of it in different terms, but the idea of self-blame of some sort is a huge issue in many of these cases. Not all, because there is no one size fits all reaction to trauma. That's all I can really say about it, and frankly it's all I feel comfortable saying because I don't want anyone to think I'm blaming the victim in any way here: I'm not and feel horrible for them beyond words.