I was fired and subsequently rehired following an investigation of a false accusation of a HIPAA violation. I lost time from work, insurance,PLO, etc. The investigation was performed after I was fired. Come to find out that I was used as an example to other employees as to consequences for violation. I've had no other disiplinary events. Do I have any rights?

If you work in an at will state then you can be terminated for no reason at all. Look at this as a suspension and move on.

You may have the right to deny this decision because it was precedent to the investigation. What should have been done with your case was to give you're a garden leave until the investigation is ultimately finished and the termination in question was based upon its findings.

You said you were fired, but then rehired,
So more exactly what did you lose.

You should have been brought back to same position without any loss of benefits. The only exception could be the pay for the time between when you were fired and rehired.

Now were you rehired because they found you did nothing wrong, or that you did wrong but were going to allow you to return

You may have the right to deny this decision due to the fact that it was precedent to the investigation. What should have been done with your case was to give your a garden leave until the investigation is ultimately finished and the termination in question was based upon its findings.

And what good would that do? The employer has the right to suspend without pay. So all this would do is stir up a can of worms that might affect the OP's future with the company.