Nanite mesh socketed to a Skeletal Mesh is not affected by the 'Owner No See' or 'Only Owner See'. Compared this against a regular Static Mesh.
The Cube is visible on the player owned character but not on the BP_ThirdPersonCharacter that was placed in the level.
The Cube is visible on both.
There's no existing public thread on this issue, so head over to Questions & Answers just mention UE-157389 in the post.