Theres definitely a setting for turning off content recognition... but... even if I say "no", I don't trust my dogs not to eat food I leave within reach.

These companies want the data, they profit from the data, they probably won't get caught if they take the data, and even if they do they won't get punished, and even if they do it'll still be worth it. You have to turn off the network or block the traffic to be sure.