No, that is an incorrect reading of the result. San Francisco is not a neighbor of Berkeley, and nobody started traveling 15 miles to SF to save a dime on Coke. The 4% increase in the comparison cities was exogenous.

I don't think we can attribute causality to the decline in Berkeley any more or less than we can attribute causality to the increase in comparison cities. If it was causal in Berkeley, it was causal in SF and Oakland. (Whose rates actually went up by like 20%? But at some point that gets cut down to 4%, I'm not sure why.)

And still: Among low income households only. We don't know what the effect was on the whole population.

Anyway, I'm sympathetic to the idea that sugar taxes work, just being critical of this particular study and your claim which is stronger than the actual study outcome.