LDH was like this. It took me quite some time to actually figure it out.
It became more and more apparent whenever he repeated stories (first he told me, then he told his mom, then he told his brother . . . and so on) especially when he was on the phone, calling one person then the other "You gotta hear this!" (Probably why it took me so long to figure it out, because I don't make a habit of eaves dropping.)
Or when we were at parties (different audiences) I noticed that every time he told the story he would add finer, more fantastical dramatic details. Embellishing the story to the point where, 5 years later, the story had changed quite a bit.
Sorry for the sidetrack, and to answer your question . . . how to handle the embellisher?
After years of dawning realization, whenever he came to me with a "You gotta hear this one!" story that sounded a bit off, I started asking him for finer details.
Me: You said that person did/said "blah blah blah" right?
LDH: Yeah! Can you believe that?
Me: What was their tone? Were they angry? Sad? Disappointed? Apologetic?
LDH: What difference does that make?
Me: It makes a lot of difference. Say the person had a bad day. What could you have done differently?
Once I started questioning the details, he either backpedaled, changed the subject or even
admitted that the situation wasn't all that fantastical and maybe he could have done something to turn it around.
Then, sometimes, we actually had a good conversations on the subject.
The above conversation isn't verbatim, but I hope you get the idea.
I don't think this approach is "calling them out." I do think that maybe it changes the dynamics of the conversation. I turns it around from "Oh, you poor thing!" to "Maybe next time you'll handle it differently."
Just a suggestion.