" Free advertising that gets more people to pirate your game is actually not good."
Or bad. Since someone pirating your game costs you nothing.
"Or is the thinking here that someone will say to their friends, "hey, I downloaded this game for free and it's awesome. But you should go pay for it"?"
Seems an unlikely conversation. Someone saying to their friends, "hey, check out this awesome game." Followed by their friends telling their own friends, "Have you played blahblah, it's amazing!" Of course, it only works if you game is actually either awesome or amazing. Some of these people will make Youtube videos reviewing the game. Strategy videos, etc. Fan art. Mods.
If on opening release nobody bought a game I made and a million people pirated it. I'd call it a resounding success. That kind of attention WILL turn in to sales at some point. Even the people who pirated the game may end up buying a copy later down the road. Contrary to media cartel propaganda pirates aren't all just about something for nothing. There are no shortage of us who simply enjoy having our cake and eating it to. Pirating content we enjoy if it is produced by people with archaic mindsets and business methods that oppose the maximum utilization of modern digital technology and sharing rather than embrace it.