No, the dream is hosted and constructed and the target fills it with his subconscious. You'll recall that when they get into the city streets dream that it is raining and they say this is because Yusef forgot to pee before going under. That's because it is his dream.
And Lukas Haas was the dreamer of the African apartment dream, from which Cobb dreamed them down to the second level of Saito's villa where they broke into his safe. When they awaken from that into the apartment Saito figures out it is still a dream because of the carpet and assumes that it is his dream and therefore he can control things and Cobb informs him, nope, they're in Haas's dream.
I'm pretty sure there was dialog establishing who was dreaming each level, but I could be wrong. I haven't seen any of the various guides popping up dispute my list, though.
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