OP - Your sole appeal to BA is that you either did not cancel or mean to cancel your ticket. You do not have any direct knowledge of what the first agent did and thus, if you make an accusation and it is unsupported, you have undermined what you want, e.g. a refund of the cancelled ticket.
If the call was recorded, BA may choose to listen to that. BA can also review the activity on the PNR and e-ticket and determine who typed what keystrokes. That would include whether you yourself cancelled the ticket. BA is well aware of its capabilities and thus no reason to focus on what it ought to do.
If it was the agent who cancelled when you requested a change, that will be obvious and you are due a full refund. If it was you, you are not due a refund, but BA may choose to do so as a customer service gesture.