The war that RIAA waged on alleged pirates is something of legend. RIAA sued people willy nilly no matter if they were living, dead, or didn't own a computer. That wide-ranging legal campaign cost tons of money.
RIAA's tax records show that the company spent $64 million between 2006 and 2008 on legal costs associated with suing people who allegedly pirated music. For all of that money spent, RIAA only won a tiny fraction of it back from those found guilty of pirating music.
During the period the $64M was spent, only $1.4M was won in the legal cases. RIAA probably figures that if it hadn't waged the battle against piracy, more money would have been lost to pirates. I always figured the people prone to pirating music weren't likely to buy music if pirated versions weren't available.