Yes, that's a pile of rubbish from the Engagement Centre, I am not going to bother with dissecting it since she was making it up.

Going back to brass tacks - as I understand it, you booked on the basis of Business + Business? You thought you had Business + Business? You got an e-ticket fairly swiftly and I'm guessing it said Business + Economy? Now you mentioned that you know about the 24 hour cooling off period but decided not to challenge at that point. So I fear that any leeway you have here is going to be constrained by not calling at that point, however the details of my first sentence may give you some leeway - if BA's IT was getting in the way of showing what you wanted to book.