I feel like you’re right, for instance depending on how you define the extra in extraterrestrial.

The space station, the Artemis capsule, microbes on interplanetary probes, etc.

It could technically be said in a sentence and be true, but it would be misleading to most people.

False makes sense if you are interpreting it strictly as "has this been proven?"

True or mostly true could easily be argued from a statistical likelihood perspective: life exists on Earth and, based on what we know, Earth doesn't appear to be all that special in a very large universe.

I think you could come up with a reasonable argument for any of the responses, hence the problem with the methodology.

No, "misleading" is a statement that is used because it suggests something else. It's a curious category because, differently from true and false, it's not about the statement itself but rather the intention behind its usage or the way it might be understood. It's frankly more of a political judgement than a matter of facts.

The prompt in this study didn't specify what does the Misleading label mean, so the interpretation varies between the models.

I mean look at the other responses here from the HN commenters. There's lots of nuance in there.