This sounds to be an example of panic and hang up by the agent. The op here is simply trying to make the nessecary amendments to his flights.
As way of background I've worked in some Public Sector contact centres. For what the agent has described as putting a marker down. This simply would not have happened in my areas of work without many layers of management getting involved and signing off on it
At least two managers would listen to the call initially and make a decision on it. For obvious reasons it would not be for the initial agent to decide and it certainly would not be told to the customer on the phone.
This sounds like very poor service to me, agent got in a flap too. There should surely be proper escalation routes in this scenario.
I have noticed that BAH are much more helpful and can make changes without a long hold than the Customer Service centre.
Strongly agree to do a SAR if you want resolution on this.