People are being biased. I could easily see Ling Qi befriending the gregarious Liling.
Also, they are white-washing Cai and Bai because they are Ling Qi's side.
I am not sure Shao would have felt that desperate if Sun was triumphant in the Outer Sect (and Tournament).
Cai-Bai alliance could have potentially fallen through, or even if it was made anyway, Sun wouldn't have lost face.
They would have been better off politically, hence no need for the adoption.
Ps.
@Thor's Twin I don't think Shao parlayed with the Goddess until the Bai Super-Squad came knocking.
I have no proof, it just feels consistent.