According to -
http://www.dol.gov/whd/regs/compliance/whdfs23.pdf
it says "Overtime Pay May Not Be Waived: The overtime requirement may not be waived by agreement between the employer and employees. An agreement that only 8 hours a day or only 40 hours a week will be counted as working time also fails the test of FLSA compliance. An announcement by the employer that no overtime work will be permitted, or that overtime work will not be paid for unless authorized in advance, also will not impair the employee's right to compensation for compensable overtime hours that are worked."
Therefore, how can they legally argue this position?
When the employer requires advance approval of overtime, the employer is implicitly stating to the work-force, including intermediate level supervisors, that employees who work overtime without advance approval are likely to be terminated for that. The employer knows that the work must be paid for, but the employer does not have to retain employees who refuse to get with the program of obtaining advance approval. Paying for unapproved overtime is the sort of problem a employer can avoid by consistent and conspicuous termination of employees and managers who do not understand that the rule is "ask first."
You do need authority to work overtime without risking being fired. However, if you do work overtime, even contrary to policy, the employer must pay you for it. You cannot waive it except by simply not pursuing it. However, when an employer has a policy like this and you violate it there is a good chance you will get a warning, a write-up, or even terminated for causing the employer additional expense in violation of the policy.
I am a California attorney and not eligible to give legal advice in your state. The following is information only, based on federal law and general legal principles. YOUR STATE MAY HAVE ITS OWN LAWS THAT PROVIDE SIMILAR OR GREATER PROTECTION. If I refer to your state's laws, that only means I did a quick Internet search and found something that appeared relevant. However, you should not rely on any comment I make regarding your state's law. You MUST check with an attorney licensed in your state.
To add to Ms. McCall's and Mr. Address' answers, one other reason employers and their attorneys make this argument is to try to get out of paying overtime. Many employees, and even many attorneys, do not know that employers must pay employees for all time worked regardless of whether it was authorized. Most employment attorneys do know this, but not every employee is represented by an employment attorney.
I represent a lot of wage and hour clients and I estimate that in at least half the cases, a defense attorney will make this argument.
