Although not in the Hippocratic oath, the principle "first do no harm" does trace to Hippocrates.
The principle is not "first do no net harm."
Doing harm while not doing any net harm is a morally tenuous proposition routinely abused by for-profit medicine. Net harm cannot be honestly assessed by for-profit medicine, or by "non-profit" research funded by for-profit medicine.
For-profit medicine invariably stilts the terms of debate to favor for-profit harm.
This is how you get, for example, Vioxx. (See the VIGOR study.)