LLMs can and will provide inaccurate answers to questions where data is included in their training sets too, that's in the nature of neural networks. It's just less likely that when the data is not in the training set...

Unfortunately most people are not aware of this and treat LLM models as this superpowered brain who knows everything and can do everything.

They will happily google it for you and give you the top reddit comment.

This is worse.

Well then it shows that these models are using widely disparate training sets and have high confidence even when they shouldn't.

Questions like "is mouthwash effective" presumably has one solid data source -- medical journals.