I don't think you read the thread, read it and apply common sense. She paid congestion charge to get there in the first place because of their fault, and again to reverse the transaction. Whether she did it straight away or not, that's £20 out of her pocket because of their mistake.
By the way you're accusing her of "smarmy money-grubbing crusade" while since the beginning she wanted to help the clerk out but was given options that would leave her at a monetary loss for their mistake. By monetary loss I mean travel costs. Then you also have to account for what this situation did on her credit score (she was notified of their mistake AFTER she put money into bank) and then you have to account that only third of the money they asked for would have been forgone if went to a different place and she was happy to hand it over to PO the whole time.
That's not what I get from the content of the thread. Did she offer, at any point, to simply bring the money back, have the entire transaction reversed (ie. both parties returned to their original positions), and her travel costs to be reimbursed on top as a courtesy? That would seem reasonable to me.
Rather, all I see is repeated rejections of the Post Office attempting to give alternate rates (which is completely unnecessary and should, indeed, simply have been rejected) and complaints that taking the money out of the bank again is just too much effort.
One would assume the easiest course of action would have been "Oh dear, mistake made": Next day, money out of the bank (same amount that went in), trot down to Post Office, speak with manager, offer to give back money for same amount given in original currency, as long as travel costs are reimbursed for the inconvenience as, admittedly, the mistake was not hers.
I don't see that approach having been made at any point, unless I've misread. Was the above the content of your friend's very first visit to speak to the manager? If it was, and he acted like the total knob you stated at first, then I apologetically rescind my earlier comment(s).
To outright refuse to merely reverse an incorrect transaction at which you are at a vast loss, however, is total management incompetence. The impression given is that your friend did not ask for this in the beginning, but impotently argued the point in order to keep as much as possible -- unfortunately against the stronger, jumped-up will of the PO manager.