Well, it was the ex who thought he was going to be killed, not the teller of the story. Telling the story as if she singlehandedly rented a stranger's couch and then was terrifed by the situation makes her sound rather foolish.
I agree. I wouldn't want to falsely ascribe foolish behavior to myself just to cut the ex out of the story!
For me, there are usually about three stages,
The first stage is when it's really raw and I'm still not quite used to the fact that we are no longer together, and I might talk about him like he's still in my life just because I'm used to doing so, and haven't yet broken the habit. (After all, don't they say it takes 3 weeks to change a habit?) That's the stage the OP's cousin seems to be in.
The second stage is where I really don't want to talk about the person anymore, and the third stage is when the ex does start reappearing in my stories--because he or she was a part of my life, and the past hasn't just been erased. The mentions just get more casual and no longer as emotionally charged. Instead of "Bob
likes bacon...sob!" like it might be at the beginning, it becomes more like "I used to date this guy who ate a package of bacon every day..."
If the idea is to move on and form a new relationship, to make stories about YOUR life be mostly about "your life with the ex" does not signal , to me, someone who is ready for a new relationship. I would think the point of the story is what happened, not that it involved the ex.
I don't think the OP's cousin is to that point yet, and it's not like she's going out on dates and talking like this to the new dates (which of course can be awkward, but is not what's happening here). She's confiding in her relative.