As an employer, you can't always wait on abefore offering a job, so you have to rely on applicants' oral and written statements to make the offer. But when the background check comes back to reveal that the person lied, you have the absolute right to terminate that individual for dishonesty.
Just make sure you treat all similar offenses the exact same way. You can't quickly fire one "marginal" new hire for an application fabrication, yet overlook the same transgression by a star employee. Such inconsistencies give great fodder for discrimination lawsuits. Here's an example of a company that did it right:
Recent case: Junet Caldor, a black male, was offered a job as a 911 operator with Onondaga County, contingent on a drug screen and. He was given a copy of the employee handbook, which stated that falsifying an application was grounds for discharge.
While Caldor's application stated that he'd never been convicted of a misdemeanor or a felony, it turned out that he did have a criminal record. He'd been convicted of resisting arrest, a misdemeanor. The county quickly fired him.
He sued for race discrimination, but the court dismissed the case. The county fired him for lying, and had warned him that lying was a firing offense. Because Caldor couldn't show that others had lied and kept their jobs, he had no case. (Caldor v. Onondaga County, No. 5:03-CV-00031, ND NY, 2006)