We're talking past each other. Your "them" is Google. My "them" is every company, many of whom do not announce the extent of their data collection.
If breaking up Google means going after every company that collects too much data, then I suggest we first (a) take a look at how much data companies are collecting and then (b) consider where we draw the line. Doing (b) before (a) would be acting uninformed and rashly.
The point is users are never going to have the power to force un-evil behaviour because the business model of data-mining companies (all of 'them', not just google) relies on social manipulation and exploiting weaknesses in human nature. Government regulation is the last resort, sure, but for this kind of business (and especially for the big players) it should be pretty damn clear by now that there is no other viable option.
Making sure a consumer's data reaches no part of a given company sounds highly impractical.
What you describe is an extremely broad scope of "opt-out". By your definition, you couldn't opt out of any company without very detailed knowledge of the company. For example, whenever you make a purchase, or just walk into a store, that data ends up in multiple parties' hands.
I doubt there is precedent for using antitrust law to allow consumers to make such refined choices. How useful would it be to silo the world in such a way?
We're not privy to the amount of data being collected within companies. Even if you break up one company that collects data, what's to stop 100 others from doing the same, particularly those in other countries?