Make no mistake. The entire site blocking mechanism of this legislation was always intended to target foreign websites. The broad overreaching scope that ignores due process and the DNS provisions, the part everyone has been mad and vocal about are the products of this. But the intent has always been to stop foreign sites.
The Pirate Bay has been the slipperiest fish to tangle with. Every attempt they have made to stop or block it, including alleged manipulation and influence of Swedish courts and law have failed. Because it's a foreign website and we have no jurisdiction over it. So they crafted this law with the intent to have the ability to block Americans from viewing it within America. The way it's worded, it's able to block anything else, too.
So since the outcry and the backlash, they have shifted their narrative to explicitly spotlight those dirty evil foreign interests. But I don't believe for a second that it was never the original goal.