How to interprete independence between treatment indicator and outcomes?
Note that this section in the book starts with the counterfactual that each agent has an outcome $y_0$ without treatment and an outcome $y_1$ with treatment. You observe only the $y_0$ of the untreated agents and only the $y_1$ of the treated agents, but both exist for each agent. If treatment is randomized across agents then $w$ is indeed independent of $(y_0,y_1)$, but of course not independent of the $y_i$ you actually observe.