Steps to reproduce:
1. Open attached project "Skin_Mesh_Issue"
2. Drag "box_3ds_Max_Biped.fbx" into Scene
3. Reveal the child objects of the aforementioned object in the Hierarchy
4. Drag in the Mesh from "sphere_3ds_Max_Biped.fbx" into the Mesh slot of the Skinned Mesh Renderer component on the object Box001 under "box_3ds_Max_Biped"
5. Observe the mesh breaking up

Repeating steps 2-4 using "box_standard_bones" and "sphere_standard_bones" respectively will not result in the same problem
Note: please see the attached video if the steps are not clear
Note 2: both objects are using the same rig

Expected result: meshes are interchanged without a problem
Actual result: the replaced mesh breaks

Reproduced with: 5.6.0f3, 2017.1.1f1, 2017.2.0f3, 2018.1.0a7