Even if true that other airlines are equally horrible, they are, IMO at least, still getting the coverage they deserve for horrible customer service.
In this case, her ticket prohibited storing an item in the overhead bin but with an exception for a "small" musical instrument. Well, if a customer doesn't interpret that vague language correctly and shows up with a violin worth likely $10s of thousands, the obvious answer is to say, "OK, ma'am, under the brand new policy you've never flown under before, a violin does not qualify. We'll make an exception today but next time buy the right ticket." So easy a child could do it, but the company had to first give a **** about customer service and not extracting the last possible penny from every traveler, which appears to be United's problem here. If they don't give a ****, and they don't appear to, then bad PR of them not giving a **** is fine with me.