The point is, that your skinning is applied on your mesh in a similar way as a texture. Now, if skin your mesh and then apply new UV coordinates, it might screw up either your textures or your skinning, apart from your texture coordinates being applied after your mesh deformations due to your skinning. Examples of errors you may encounter are a texture that "swims" on your character.
Changing the inputs of your UV mapping happening before your skinning might help, but that