Under EC261 and the Mennens judgement, the passenger is entitled to reimbursement (not compensation) of 75% after deducting necessary taxes, which on that route is about $33. So assuming this was a one way ticket and no other unmentioned complexities, that is about $53 or so, plus 30k Avios refunded.

Because it's a refund off the original tickets, airlines tend to say "go to the original ticket company to get this reimbursement, they have your money". 101% BA would say this if it was the other way around. However in law, it's the operating carrier that should pay this and seek reimbursement from their airline partner under Article 13. It's the last clause that they hate doing, and I can actually appreciate that from a cash management perspective it's very tricky to do this for relatively small sums. Plus the Avios are actually part of a third service company organisation called IAG Loyalty. The OP can rightly say "your problem, not mine" but I'm focusing on expediency here.

It is also the case that you have to actually be downgraded - travelled in other words - to get Mennens. So you can only claim in advance if this is treated as a cancellation and you decide to decline the rebook option. Hence you were correctly advised to only claim after travel. And initially you should work with BA to make that claim, stating very clearly it's a Mennens claim, otherwise this will just get treated as an Involuntary Refund, and thus merely a fare difference of less than half of the amount to which the traveller is entitled.

Airlines choose this system, and BA is totally complicit in it, so I would urge the traveller to seek every cent of their EC261 entitlements. And reject (as legally incorrect) that Mennens only applies to downgrades at the gate, not advanced notice downgrades - something else airlines are known to do despite the clear wording in the Regulation. Unfortunately if BA doesn't give the full amount, then it's Iberia that is ultimately on the hook.