CLEAR doesn't do any background check. You are just paying to get your own VIP line up to the checkpoint. You still have to talk to the TSA agent and show your ID. CLEAR doesn't even get you to the front of the precheck line unless you've paid for that as well. The line for precheck is usually shorter and quicker but you still have to talk to the TSA agent. The precheck checkpoints will usually just use metal detectors instead of bodyscanners and you get to keep your shoes on and your electronics in your bag, overall making the line move quicker.

The TSA does publish a list of disqualifying items for Precheck. As long as you fill out the forms truthfully, the disqualifications pretty much all revolve around the questions "do you have a felony record?" and "are you on any interpol or government watchlist?" If the answer is no to both, chances are you'll pass the precheck investigation. It's not like they send out agents to talk to you neighbors, friends, and coworkers so it's really just a records search. If you're on a government watchlist, you've got bigger problems than long lines at the airport. Of course there's always the situation of mistaken identity but there's already a system in place for that with the DHS redress numbers.

If you routinely get SSSS on your tickets, it's probably a good idea to get a redress number. Even if you do get precheck, there's still a possibility of getting demoted to regular security and a possible SSSS stamp if something about your trip is "suspicious" like multiple one-way tickets booked for a non-family group.