Your state 3 should be "Has opinion B but has been exposed to a node in state 1". In that state, the next exposure to different node in state 1 would change the

Your state 3 should be "Has opinion B but has been exposed to a node in state 1". In that state, the next exposure to different node in state 1 would change the node to state 1b. True believers win by being immune to contrary opinions. I doubt the researchers were motivated by headlines. Rather, they put together a simplistic model and got a simplistic result that is surprising only for the consistency of the tipping point across their chosen variations of the model. For example, other (field) research shows that the common reaction to opinions or facts that contradict one's opinions is to argue, which tends to cement one's opinions further. This doesn't necessarily imply one starts out committed. It also ignores confirmation bias, which limits exposure to contrary opinions. Etc. As others point out, if their model was accurate, there could be no long-term stalemates, like progressive vs. conservative, both of which have significantly more than 10% true believers. Nonetheless, it is suggestive, particularly as it describes relatively isolated communities and as it implicitly distinguishes between belief systems which insist on absolute commitment (e.g., Evangelicals, Tea Party) vs. those which are satisfied with mere agreement and tolerate dissent (e.g., Ecumenicalists, Independents).