Simplification bias-- this one might be standard, but if so, I don't know a usual name for it.

It's mentioned in NLP that people tend to drop "frames"-- if something is said, people will react to it as though the speaker is endorsing it as true, even though the speaker might be mentioning it as something someone else said.

The link describes people treating a possibility as a certainty. One flavor of this is called catastrophizing, but I don't think that sort of simplification necessarily leads to anchoring on the worst possible outcome.