Copyright infringement threats very rarely represent the interests of authors or composers. I have dealt directly with other rights clearinghouses (never HFA) assessing claims of infringement whose claims were rebuffed when the authors were consulted.
In my case, I did find it necessary to find a lawyer. Investigating the "fair use" clause of copyright law, which includes parody, became the basis for what would have amounted to a defense if the had taken us to court, which they did not.
First and foremost, though, remember that these people don't represent the law, they represent money and a lot of lawyers and corporate scare tactics. They can never shut down the database, only force you to not "publish" lyrics of their "clients". Whether you actually "publishing" or they are actually representing their "clients" interests are different legal matters all together. Intellectual Properties Rights will become the hottest topic of the next decade now that big corporations have recognized the power of the internet and the ways they can control it. Either copyright law is going to be turned on its head or the internet will become a silent fizzle. Big business doesn't want that eiher.