Well... ***technically*** one could be honest and fail a background check...
"Yes, officer, I wasn't paying attention and ran that red light."
"No, I didn't realize that my ex could accuse me of kidnapping our child when it wasn't my visitation day."
It's also possible for a dishonest person to pass a background check if they've never been caught...
Naturally, these are absurd examples, but considering I pay for my own background checks each year and get a piece of paper that effectively says "This page is intentionally left blank", I find background checks to be absurd in general.
The only thing a background check gives is a history of what has already happened. Technically, it's a document that's out of date the moment it's generated.
--Tom