How come it's "safe" to take the nuclear stuff for a nuclear medicine scan?

SMALL DOSE. It is relatively safe to take nuclear stuff for medical reason because the information you receive from the nuclear medicine scan (benefit) outweighs the small risk (small amount of radiation) that you receive from it. It has less risk that an x-ray, less risk than cigarette smoking, less risk than flying from new york to los angeles, and less risk than spending a day at the beach under hot sun.
Radiation low. The amount of radiation received is acceptable dose if information gained from scan outweighs any radiation risk and helps diagnose problem that then can be treated appropriately.
We think very. Like lots of things, excess can be harmful but in small doses there is no harm. We say it is "safe" because there is no evidence that it causes any harm. Research of course is ongoing but in low doses, radiation has not been clearly shown to cause harm.
Tiny dose. Most of the rays pass through your body without depositing dose. Those rays are available to the camera to make the diagnostic image.