As far as I can tell, there is no such insight here - in the middle of page 13 they admit that in their solution, the weak energy condition is violated, and eve

As far as I can tell, there is no such insight here - in the middle of page 13 they admit that in their solution, the weak energy condition is violated, and even that: "No amount of modification to the configuration could get rid of these WEC-violating regions." If I'm reading this correctly, all they have done is found a solution that has positive Eulerian energy density according to one particular reference frame, but not according to other reference frames. (I'm not a physicist, so please correct me if I'm wrong.)