Verbal voice and responsibility for the act
Hypothesis examined: the Qur'an would use the active voice to attribute an act to its author and the passive to remove that responsibility by erasing the agent.
The hypothesis arose from 1:7, where the contrast is striking: « أَنْعَمْتَ عَلَيْهِمْ » ("You have blessed", the agent is named: God) against « ٱلْمَغْضُوبِ عَلَيْهِمْ » ("those who incur anger", no agent named).
But the Arabic passive has many other reasons than removing responsibility: the agent may be obvious, known to all, or beside the point. In 2:183, « كُتِبَ عَلَيْكُمُ ٱلصِّيَامُ » ("abstention is prescribed for you") is passive, yet there is no doubt about who prescribes it: here the passive removes no responsibility at all.
The announced test ("passive participles followed by عليهم or a complement") was never carried out, and the rule rests on an interpretation of motive that the text can neither confirm nor refute. The translation principle that remains, not adding an agent where the text has none, is a matter of method and needs no rule of its own.
In the text
أَنْعَمْتَ عَلَيْهِمْ غَيْرِ ٱلْمَغْضُوبِ عَلَيْهِمْكُتِبَ عَلَيْكُمُ ٱلصِّيَامُ