I would suggest you're over-thinking it. The essence of it is "we think you're a bot because you haven't given us enough private information about yourself".
Exploiting that information is Google's core business, and it doesn't like people evading their panopticon. So they're no making life harder those who care about their privacy.
Not surrendering your data to Google? We'll treat you like you're not even human, and through reCaptcha we'll tell thousands of other websites to do the same. That will teach you to hide things from the all seeing eye of Mountain View.
Exploiting that information is Google's core business, and it doesn't like people evading their panopticon. So they're no making life harder those who care about their privacy.
Not surrendering your data to Google? We'll treat you like you're not even human, and through reCaptcha we'll tell thousands of other websites to do the same. That will teach you to hide things from the all seeing eye of Mountain View.