Looks like I had a few memory errors. First I forgot that in the first phase, when they were able to identify people using DMCA subpoenas, they had a used a mix of suing first and offering a settlement first.

Then in the second phase when they lost the ability to identify people that way they switched to filing "John Doe" lawsuits, which then allowed them to get subpoenas to identify who owned the IP address where the uploads came from.

I'd completely forgotten about that. In most cases they offered a settlement once they had a name but still, there was a lawsuit. (If they couldn't get a settlement, or didn't even want to ask for one, they could amend the lawsuit to name the real person and proceed).