Despite suing the wrong person multiple times, the RIAA has always pushed back when asked to pay for the legal fees of those wrongfully sued.
Tanya Andersen has fought back pretty hard on that claim (and then sued the RIAA separately on other charges as well).
Despite multiple tries, the court has repeatedly sided with Andersen pointing out:
Copyright holders generally, and these plaintiffs specifically, should be deterred from prosecuting infringement claims as plaintiffs did in this...