As far as I can tell from the evidence given in the talk, contagious spreading of obesity is a plausible but not directly proven idea. Its plausibility comes from the more direct tests that he gives later in the talk, namely the observed spread of cooperation or defection in iterated games.

However, I agree that it's probably important to not too quickly talk about contagious obesity because (a) they haven't done the more direct interventional studies that would show whether this is true, and (b) speculating about contentious social issues in public before you have a solid understanding of what's going on leads to bad things. He could have more explicitly gotten at the point that we're not sure what effects cause the correlations that we see- I caught it but I suspect people paying less attention would come away thinking that they had proved the causal model.