Ice dam, water behind the walls etc

[George P.]

Had a mysterious leak in the basement's ceiling when it snowed heavily this winter.

I have asked for the community input a while ago (https://www.biggerpockets.com/forums/67/topics/183...), and finally one of the contractors gave me a possible reason. 

According to him, the water has built the ice dam where the neighbor's gutter touches the party wall. He thinks realigning the gutter will solve the problem. Does it make sense to you?.... 

The spout is still on that end and I would think the water would still come that way?..

Attaching two pictures. Thank you in advance!!!!