The part of the law quoted is only a small snippet of the law. Many states now also keep a database of prescriptions for specific controlled substances for use in finding and tracking irregularities. For example, in Texas, certain drugs such as Adderol or Oxycontin are written only on specific prescription forms. The form can only be picked up at the doctor's office and the prescription can only be filled once every 30 days, usually based on the dosage and at the number of pills to make up that dosage.
And, up until this year, in Texas, the form used to be in triplicate with one copy going to the state of Texas. (I don't know how the state of Texas is now notified without the triplicate form, but I'm assured that it is.)
Of course, this is done in Texas and Rush is in FL. But when it comes to controlled substances such as the amphetimine based Adderol or opiate based Oxycontin, I would be surprised if FL didn't have some kind of similar system for tracking prescriptions of controlled substances.
So "grandma" may not tell the next doctor about what she told the last doctor. But I'm willing to bet the state of FL will know.
My guess is that information from this database was the basis of the seizures to begin with. The state's attorney is probably trying to find out what was not reported to the state of FL. The reports of the hundreds of thousands of Oxycontin pills Rush was said to consume probably formed the basis of probable cause as there is likely no where near that much reported to FL.
BTW, I'd be real surprised to find a grandma going outside of her HMO's PPO to buy outrageously priced prescription drugs as many times as she wants just to have the drugs. She'd be better off going to Canada or Mexico and buying mass quantities.