Counterpoint, all the FP replacement effects like
Mighty Steed specify that the companion must not be assigned in the game text. Assignment actions don't do that because the rules do it for them.
In fact, even
Return to Its Master can break an assignment rule: you can assign a non-fierce Nazgul to skirmish the Ring-bearer during the fierce skirmishes, even though the rules say "...ignore any effect that results in assignment with a minion that is not fierce." But that's because the rule is "
During the fierce assignment phase, ignore any effect that results in assignment with a minion that is not fierce." Similarly, I think it's pretty reasonable to exempt
Mordor Assassin from any assignment action restrictions.
The assignment cancelling may have instead been to prevent 3 copies putting 3 Nazgul on the Ring-bearer without bothering with trying to shape up the wordiness of something more specific such as "and if the Ring-bearer is assigned to a skirmish, cancel that assignment. Then assign a Nazgul..." Or perhaps make sure that Gimli or Legolas with their weapons don't win a skirmish against a
Goblin Runner or
Morgul Skulker and kill the Nazgul with the trigger. I personally have always enjoyed the idea of it too, that all focus turns to The One Ring and the one who holds it -- even among the players.