In practical terms businesses are required to collect employee PII in order to comply with various regulations. But that's not "entitled" that's "government imposed for unrelated reasons". (Those unrelated reasons being illegal aliens and tax compliance.)
There's also an element of risk management with the employer wanting to run a background check. But there's no particular reason that can't be done via a mutually trusted third party, similar to escrow. In fact it often is done that way in the residential rental business - the applicant authorizes the check and pays the third party who then furnishes the report to the landlord.