For me, personally, Leliana's song is just a story. Sure the characters of Sketch, Tug, Dorothea, and Marjolaine were there and the root plot points are real but the events embellished, the setting I believe would change with the audience. We're familiar with Ferelden so that's it's setting. If she was telling it to a audience of Antivans it would probably be in Antiva City. It's like when hollywood says "based on a true story' you get some facts right but a lot is just for the audience's entertainment.
So I think what she says to you in Origins is the truth, though leaving out Sketch, Tug, and Dorothea because she's still fairly guarded about it.
In The World of Thedas vol. II [Chapter Three] under Leliana's section it has a letter to Sketch called "We who did not belong" and the first two lines are this:
"Do you want to know a secret?"
That was how I started when I toyed with stories as well as lives.
It continues on with her apologizing to Sketch for how she always embellished the story (the two seemed to have a falling out over it) and her saying she has been trying to learn more about Tug's life so she can honor his memory better.That phrase is how she starts Leliana's song so this and the letter causes me to believe most of it wasn't true and to trust her word in Origins.
Though if Leliana's song is true, the point about the City Elf's mother calling her a child could mean any age, my mom still calls me child and I'm an adult. In order for the timeline to be consistent though the City Elf's mom would have to have died shorty after the DLC and so that puts her death only 2 years before Origins as that's when this event takes place.