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These drugs are what's known as "non controlled" prescriptions. In general use, 'controlled substance' means those drugs which are 'scheduled' - meaning they have special restrictions above and beyond those of ordinary prescription drugs. These restrictions include additional limits on handling, storage (they have to be kept in locked containers), and record keeping (you need a special book which records every single dose). The most tightly controlled, Schedule I, includes those drugs which have little or no medical use - this includes most illegal drugs. Morphine is Schedule II; it has some legitimate medical uses but handling is controlled because it has a high abuse potential. Prescriptions of these drugs are closely monitored, and would need oversight to re prescribe (and would need original, rather than faxed, prescription documents).
For non-controlled prescription medication, there still needs to be a doctor that prescribes them, but often they won't require reassessment for 6 to 12 months. A good example would be birth control medication or thyroid medication. It is watched, but not "supervised" per se. Rather, re issuance of the prescription is often done with a call, and doctors that are not the primary or prescribing doctor CAN refill prescriptions. If it were a controlled medication, this could not happen.
And whether it would be legal to take medicine that was prescribed, yes, it's absolutely legal. Now if the prescription had lapsed and she procured the medicine from the streets or otherwise illegally, that would be prescription drug abuse, which is illegal. It's not a requirement that someone be under a doctor's control, but rather that the prescription itself be legally obtained.
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