what...? Your example is a convoluted extension of the police-officer example except you added the dog element which I think most people agree is messed up... but that's a separate unrelated issue to address.
I'm saying if you have a private/secret meeting in your basement about how to overthrow the government there is no parallel construction you can make to intercept that. If you have secret files on your computer you can't have cops "accidentally" bump into them.
I'm really doubting "you will never have information that's so secret that you can't build a parallel construction"