Still not buying that linguistic "fact". As in many cases in the language, there is a referential gap, and consequent ambiguity, when one couples a verb and noun into a single term because the relationship between the two is no longer clear. The noun may be either the agent, the recipient or the instrument of the action. The language is not consistent in the case of either murderer or beater (or many other such words); consider child-murderer, where child may be either the agent or recipient, but is unlikely to be the instrument, contrasted with ax-murderer, where it is naturally understood as the instrument. With "beater", all three are possible (though agent is least likely), and context is what determines the sense, not some fictitious linguistic rule.

Hence, "banjo-beater" may be either one who beats banjos or one who beats using a banjo, given the limited ways English provides for combining such elements. Without further information, you might leap to one meaning over the other (after all, what is more natural than wanting to smash a banjo?), but the original reporter is not wrong in his choice of the term. You would have it that the miscreant could only be labelled a "wife-beater", but spousal abuse is fairly common, whereas inflicting pain (physically) with a banjo is not--for this reason, "banjo-beater" is not only correct in this situation, but rightly places emphasis on the more newsworthy aspect of the story.