Most big background check service companies are checking your criminal history directly with the court houses of where you’ve told them you’ve lived. Many will also verify your past employment directly with those companies as well. Depending on the company/job title they may also be checking your credit score/bankruptcy history or verifying degrees with universities as well. They don’t care about what data brokers have on you because they’re getting verification on things directly from official sources.
I don’t know if you’re worried that your too “locked down” privacy wise for a background check to clear? I wouldn’t worry because if you’re using your countries equivalent of a SSN and living “on the grid” but not online at all they’ll still be able to get the info they need/want anyway. I’ve had employees who didn’t even have emails or own phones/computers clear background.
The background companies we go through here in the US aren’t “random people” and you sign a release of that information for them when they start that background check. So you’ve given them permission to access that info on you. I don’t know what HRs your dealing with but if it’s random hiring managers asking you then they have no idea what’s in a typical background check anyway.