Suppose a lot depends on what you think a 'supporter' is. If your model is that of a consumer, with the language of 'purchase', 'customer satisfaction' and 'rights', then booing follows naturally. If you buy a flat screen TV and it has problems, you'd go back to the store and give the seller an earful. It would be your right; what you purchased is not up to scratch.
Personally, I think of a supporter as something different, less on the model of consumer rights, and more along the lines of an identity, a shared fate that extends over time and doesn't follow market logic. There is a weird way in which booing would be for me, booing myself, rather than rolling up my sleeves (or at least thinking about how to make things better), but I don't suppose everyone shares that view. Rocketing ticket prices and commercialism have changed perceptions a lot. One thing I would say is that it's hard to claim that booing is making things better.