My view is naturally enough that my interpretation is the simpler one that leads to the most reasonable result in the OPs question above and is closest to RAW. If my argument does not convince you, I think we have to agree to disagree. As long as you can get your game to work with another interpretation of opportunity action, its not really important what I think. What IS interesting is that the rules, even in the 4th editions, can be so unclear on so many points and would dread being the judge at a competitive event where these rules came to the test.
On page 268, under triggered actions, the PH clearly states that while OAs and Immediates REQUIRE a trigger, free and non actions can also be triggered actions. So, no, I don't think you can RAW in a rule that all triggered actions must be OAs or Immediates.
To put it another way, If OAs and Immediates are squares, and triggered actions are rectangles the PH says:
All squares must be rectangles.
From which you appear to have derived the rule that all rectangles must be squares.
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On the next page under Action on Other Turns that free actions are allowed (as many as you want actually) on another's turn, and it explicitly lists free actions alongside oppourtunity actions and immediate actions as another and seperate type of action which can take place on another players turn.
So the general rule is that free actions can occur on another players turn. Here a specific power creates a specific rule that there is an attack, which is a free action, that must be triggered before it can be used. It is a triggered free action, which means many of them could take place on an opposing creatures turn. Thus -- the general rule that you could use that free action that the power grants you over and over is limited by the specific rule (the trigger requirements) ... but that's it.