Boltzmann brains and multiverse are logically distinct issues. A single universe with an eternal de Sitter future potentially has this problem. I regard any theory that predicts a Boltzmann brain majority as wrong, but it's not clear how generic a prediction this is for eternal inflation, or even whether eternal inflation is the right cosmology (e.g. for the test case, Vasiliev gravity).
Leading inflationary multiverse theorist Andrei Linde (and others) gives significant enough credence to the Boltzmann brain problem to tweak some of the parameters of his theory (here for example http://arxiv.org/abs/hep-th/0611043). Are there more elegant ways to deal with the issue that LWs are aware of that would not require changing physics to accommodate?