There seem to be three kinds of parties here, the advertisers, the exchanges, and the websites. An advertiser places targeted ads with exchanges. The websites send bids, potentially with user info, to the exchanges.

I'm finding web pages at Google showing that they run their own ad exchange, and they integrate with other people's ad exchanges.

I don't know how to find out if Google makes bids using any exchanges other their own, or whether the information from Google's bids could otherwise leak to advertisers.