Hmm... Interesting points you raised.
I feel like I have done this at least once before on AA where they re-calculated the fare from the original fares that were in the market even after having flown the first segment of my return journey. The last time I was in this situation, I had a fare DUB-NYC and flew DUB-LON only. I ultimately wound up having to change LON-NYC to a future date a couple of months later.
That said, I don't remember if they added a stopover, or re-priced using end-on-end fares DUB-LON and LON-NYC. What I definitely knew though was waiting to make my decision until LON didn't forfeit the remaining value of the ticket.
I see your point though, that it may be difficult to argue retroactively inserting a stopover on a HKG-NYC fare after the first segment has flown.
Though at the very least, a retroactive end-on-end fare construction to determine the future add-collect should still be possible. i.e. I shouldn't have to lock down my dates tomorrow, but just be prepared to pay a difference in fare down the road applying the residual value of the ticket to the new price.
That last part is what the agent insisted was correct and I am struggling to believe she was right.