When a medication has been clinically proven, it's been tested on actual patients. Clinically can also describe a cold and detached manner, a personality better suited to robots than people.
It's a good thing when doctors and scientists do things clinically, because they're not only using studies and statistics to make decisions — they're talking to and observing patients. On the other hand, when a doctor treats you clinically at your yearly appointment, she is efficient but aloof, rather than warm and welcoming. Clinically is from clinical, from the Latin clinicus, "physician who visits patients in their beds," with the Greek root klinike, "at the sickbed."