What is the word for a shocking statement that lacks facts to back it up. E. g. someone talking about climate change and saying “we are at the beginning of a mass extinction” without providing any further facts.

The word used for such statements as described here is sensationalist.

Explanation:

Sensationalist statements are those that are designed to gauge reactions out of people and not necessarily raise the level of, or contribute onto any meaningful discussion in any way.

The statement has no semblance of facts to back it up and is often very exaggerated form of a truth that has been convoluted beyond its sense so it serves only to rile people up and not to make them discuss things.

It is often used in rhetoric to drive the points away from discussion and make speeches out of debates.

the answer is decimated