Udpate: United Airlines has responded. Bottom line: YouTube complaint videos appear to work.
Instead of a complaint letter, the band "Sons of Maxwell" have posted a music video aimed at United Airlines over the destruction of one of their guitars on a trip last year:
[We] were traveling to Nebraska for a one-week tour and my Taylor guitar was witnessed being thrown by United Airlines baggage handlers in Chicago. I discovered later that the $3500 guitar was severely damaged. They didnt deny the experience occurred but for nine months the various people I communicated with put the responsibility for dealing with the damage on everyone other than themselves and finally said they would do nothing to compensate me for my loss. So I promised the last person to finally say no to compensation (Ms. Irlweg) that I would write and produce three songs about my experience with United Airlines and make videos for each to be viewed online by anyone in the world.