Question about private polygraph test

[paulnelson]

I read one strategy defense attorneys can use if a defendant is falsely accused of a crime is to have them take a private polygraph test. It is not for submission to a court. If the defendant passes, the defense submits the results to the prosecution and requests the charges to be dropped.

Sometimes the prosecution will want to administer a second test in their office and if the defendant passes again, they will agree to drop the charges.

If the defendant fails the first test, the results are simply kept confidential.

Has anyone ever heard of this? If this is possible, why would BK not do it if he is really innocent as he claimed when arrested?