I'm not sure what losing a scout has to do with Babcock. His involvement with scouts would be minimal at best.
Shanahan would be the one who poached him, but I think it has more to do with him getting a promotion he was never going to get in Detroit. The Wings have Hakan as their director of European Scouting and I'm sure Shanahan was well aware that Vuori has spent the past few years learning from him. Who better to choose to become your own director of European Scouting?