"I'm pretty sure that does NOT mean a warrant specifically naming each person whose information was collected. Or does it?"
Nobody (here) knows. This conversation is more heat than light in part because people are spouting all sorts of uninformed nonsense just to perpetuate their theatrical sense of outrage.
What I've read so far suggests that there's some sort of FISA-related oversight of the "reports" generated by PRISM. It sounds like analysts can do queries based on certain rules that are designed to include only conversations with foreign participants, but to get detailed information they need to go through a FISA court.
Honestly, though...you can't tell much of anything from the documents that have been leaked. Most of the details you see people discussing here are speculation, or worse.
I know for a fact is does not. Even with the traditional criminal warrant (say a mafia boss) they only need a warrant for ONE person on the call.
You need a lawyer to translate anything our leaders (biz, gov or other) say. It's all form with very little substance. If you thought you heard something definitive you almost certainly misunderstood.