It is illogical. The only explanation that is likely in the slightest is that somehow the HRE is seen as the successor of Rome; foreign powers leave the imperial territory they conquer in the empire because only then can they themselves be elegible for the position of Roman emperor, presumably the most prestigious title in Europe.What I really don't understand is that territory in Southern Italy they have, I can see invasion or soft power in the North, but the South is utterly confusing me, and that's saying a lot!
On further look Denmark also seems to have territory in the empire. Ugh, my head is spinning trying to figure out this monstrosity. What kind of empire has foreign powers controlling a sizable chunk of its territory?
As for Southern Italy, perhaps France helped it revolt from the Christian radicals in the Papal States and in return they elected a second son from France as king? Though that would imply a much greater degree of feudalism and monarchism than IOTL.