The actual charge was "maleficium", using magic to harm people. Things like poisoning also counted, although we wouldn't consider that magic today. The important point was the intention to cause harm.
Of course that was hard to prove or disprove, but we have examples of alleged witches accepting payment for harming/killing other people using whichcraft - like a contract killer. So at least the intention to cause harm was there in some cases.
There are numerous accounts of people having (alleged) supernatural abilities who was not persecuted, e.g ascetics surviving without eating for years and such. These were generally held in high regard, and could end up as saints.
Of course people could be accused for maleficium on really flimsy evidence so it could also hypothetically happen to the hypothetical slow-aging person just like it could happen to anybody else.