Your part worked! I tried to use your explanation to modify my version and still had no luck to get it working. By comparing your modified version to mine I found the problem and got my version working too: fritzing isn't able to handle transform attributes in SVGs correctly. As soon as I removed the transform attributes (calculating the correct coordinates to apply the transform) fritzing was able to handle my SVGs with millimeters too.
Thanks a lot steelgoose for your modified version as it helped me find the true reason for the falsely applied copper fills!