Not sure what you understand by "against company". For me Doors of Night played during M/H phase of some company is against the company, like against Hazard Limit of the company. Not "on" but "against".
If Trouble on All Borders on own faction is OK, then placement of faction card in hazard player's area is not obstacle.
Unless it becomes OK because it may also affect hazard player. Then we have a concept of estimating a validity of play basing on what would be effect if some card will be eventually played. If the effect would be such a such, then a playing of the card is OK (even if generally it is not allowed), if the effect would be other then playing of the card is not OK.
Neither so Ancient Nor so Potent in first place overcomes restriction "an action may not target a card not in play".
It forces an opponent to take target item to hand. Is not restricted to opponent's item. If played on own item, the opponent will take hazard player's item to hand. In multiplayer it is not known to hand of which opponent (opponent is not tied to owner).
If it is against an intention of the creator then make errata. Replace "Playable on a stored item." with "Playable on opponent's a stored item." .
Alternative is attempt to create a justification of invalidity of playing the card on own item. Complex system of traps and exceptions that would pass Trouble on All Borders on own faction (despite of general restrictions) and would stop Neither so Ancient Nor so Potent on own item and Muster Disperses on own faction.
P.S.
Returned Beyond All Hope is not restricted to hazard player's Maia permanent-events.
Strange or not, I can live with it because I know to which player's hand the event will be returned. I know how to handle the situation when I take opponent's card to my hand; there is no limbo state.
Of course if there is a rule that prevent a taking of opponent's card to hand I would want to know about the rule.