Talking of agents advice, I worked for a hotel company many years ago and we had a few special package rates - and the cheapest was always Sunday for two nights.
One day someone called me asking for a stay for Saturday for two nights, lets say the price was GBP295. Trying be helpful, I told her that there was a special offer on Sunday which was GBP 99 for 2 nights. She booked four rooms. I think they were non refundable.
The next day, her mother called me screaming that the company had lied to them. They couldn't get flights cheap enough (because at that time there were still Saturday night stay restrictions on most flights) so she booked Saturday back Monday, and wanted the Saturday for two nights at GBP 99, not GBP 295.00, which I could not do.
Lessons:
- the initial caller couldn't even remember my name... but she remembers I sold her a dud deal.
- my advice was based on my knowledge of the product I was selling, not other aspects of what the caller needed to get there.
- as an agent I stopped making suggestions that could save people money because there were so many unknowns.
- advice you give will nearly always be misunderstood
So I see why the BA agent answered truthfully that you should cancel and rebook, without necessarily going into detail. Or, expecting the OP to call back to cancel since they'd used this method of contact before - perhaps she thought she'd get a chance to do that.
I had to apply to cancel a booking within the 24 hour window recently, and saw that screen about "BA's refund decision is final" and took fright and called them to cancel!