[gtop3]

The FDA approves medical treatments, many of which are chemicals. They approve treatments based largely on how effective it is as treatment. It's safety profile is studied and considered in a broader context. Many drugs approved by the FDA are incredibly blatantly unsafe. The FDA spends non-trival amounts of effort communicating risks associated with chemicals to doctors and patients.

Outside of this example, proving a negative on this scale is a 1000x larger problem than proving there are no leprechauns. No one has proven there are no leprechauns. It is logically possible to prove a negative, but we simply cannot observe all of the places a leprechaun might be hiding at the same time. The best thing we can do is list off all the places we know there are no leprechauns. This is very different than "proof".