(Spoilers Main) What was even the point of telling this story?

In ACOK, when Jon first meets Ygritte, she tells him the story of Bael the Bard.

To put things briefly, the story is about a wildling who went to Winterfell and sang for King Stark and fell in love with his daughter, who he ended up disappearing with the next day. After that, the entire North was out searching for her, even the Night's Watchmen went beyond the Wall to look for her, but to no avail. Finally, when the Stark returned home after searching for her, he found her sleeping in bed with a baby in her arms. She'd been in the crypts of Winterfell the whole time. Her son grew to become the next lord of Winterfell and KITN. Years later, he led the northern hosts against an army of invading Wildlings, led by Bael was KBTW. But when they met on the battlefield, he couldn't kill his son, and the Stark slew his father. When he returned home, he presented Bael's head on a spike to his mother, and she lept from the tower of Winterfell in her grief.

Now, what makes this story so unique is that it bears much resemblance to Robert's Rebellion,

1.) The singer of royal blood steals the Stark maiden away.

2.) Entire wars are fought to rescue her.

3.) The Stark lord finds her in a bed of blood with a baby.

4.) A woman commits suicide after learning about the death of her loved one.

What also makes it interesting is that of all the stories Ygritte from beyond the wall that Ygritte could've told Jon, she decided to tell him this particular one. Why is that? Is it possible that the story has more meaning than many people might think it does?

Now, there is already a theory Arthur Dayne never died, and that he's really Mance Rayder in disguise. Hypothetically, if this theory is true, then is it possible that he told the Wildlings about Robert's Rebellion, and that it inspired them to come up with their own spin on the events? Because if so, then where did they get the idea that the Stark maiden was hiding in the crypts the whole time?

If the whole Mance/Arthur Dayne is true, then is it possible that Rhaegar and Lyanna were hiding in the crypts on Winterfell the whole time? Think about it.