True, but the DMCA requires a takedown notice and then failure to comply before anything can be done. SOPA allows pulling of DNS entries as a first action, meaning sites are down while they handle the complaint. There's also a huge difference between "liable" as the DMCA defines it (must remove when notified) and "liable" as SOPA defines it (must remove immediately, notification == site death)
The private right of action in SOPA is actually modeled on the DMCA notice. Let's say a record label asks PayPal to stop payments to an allegedly "infringing site". PayPal must notify the allegedly infringing site of that request within 5 days. If that site provides a counter-notification, PayPal leaves the site alone and checks out of the whole process. From that point, the record label has to go to a judge to try to get an injunction against the site (with all the associated burden of proof, etc).
The DNS blocking is only available to federal law enforcement; a private complaint can't pull DNS under any circumstance.
