_When misrule takes its place at the eight corners of the world
When the Brass Tower walks and Time is reshaped
When the thrice-blessed fail and the Red Tower trembles
When the Dragonborn Ruler loses his throne, and the White Tower falls
When the Snow Tower lies sundered, kingless, bleeding
The World-Eater wakes, and the Wheel turns upon the Last Dragonborn._

^This is the Dragon Born prophecy. 

It notes the return of the last Dragonborn. 

He returned and he died, the prophecy did not state that he'd/she'd succeed, hence the prophecy was actually correct, as you accurately stated.