You need to be terribly careful before you brandish that sort of accusation, even though I can see why you do so. If you are wrong, and I believe you are incorrect, then it dents your position mightily.

You are a highly experienced BA traveller, so you must surely know by now that agents sometimes offer the best option that they are aware of, and that's not lying, that is what they see in front of them on their screens. It's up to you to use your powers of analysis, persuasion or indeed the legal process to secure a better outcome. If you think about it, even if the Amex side is correct, there's nothing to stop BA having a dialogue with Amex about this, or alternatively to offer you an equivalent voucher with a similar, or better, outcome.

You will have had plenty of e-vouchers in your time so there's no excuse for you not to understand the system by now.