Yes (as above). The point is that UA made a promise (and even gave out a confirmed seat/boarding pass). If they fail to keep the promise, they must give compensation. It doesn't matter whether the original compensation was "fair" or whether the agent (whichever one) made a mistake: that is UA's internal business, not the customer's responsibility. ...However, your friend might tone down the letter and shorten it a bit for greater effectiveness (you should take out the name from this posting but include it in the final letter).