Lost in translation?
Having read the ruling of the court (in the original) I would like to mention that the court in fact thinks that the husband was using the internet connection to share files(as seems likely by the songs offered). If the defendant would have been willing to identify/name the users responsible or possibly responsible she might not have been charged. Since she remained mute on this point the court sees her/her husband liable.(2.II.b )
Lack of supervision was mentioned only as "auxiliary reason" (hope this is correctly translated into english) explaining that the parents knew the possible dangers, Despite this awareness they were incapable to check the actions of their children. Since the children were aware of this incapability this resulted in effect in a complete lack of supervision in this point.
Unfortunately the court does not explain what measures would have been required and even mentions that this ruling does not set standards as to liability of the owner of an internet connection if a third party is using it for unlawful purposes like sharing of copyrighted material.(II.2. 2nd paragraph).