painting problem with a mesh

I will explain it as simple as I can.

Thos mesh just don't want to be painted. When I mark seam it, and I average island size and pack island for every meshes, it gives that result: 

Picture file 1

But as soon as I just smart UV unwrap it and paint on it separately, it gives that nice result:

Picture file 2

This is the blend file. You can try everything to make it work. I just can't compile with that mesh. I really don't know what is happening with this.

Blend file

I can choose to ignore the problem and make another mesh, but I would like to know to learn more about Blender.

Thx for reading me!