You're not thinking about this probabilistically. This isn't about "correct" and "incorrect". There is an entire universe between those two poles with regards to most kinds of knowledge. Facts are a specific kind of knowledge, and frankly, not that important. It's more important to know why the Civil War was fought than to know the exact dates and locations of each battle.
I've heard people say they wouldn't use ChatGPT even if there was "only a 1 in a billion chance that it made their bank account details public"...
May I introduce you to some very real probabilities:
https://oddsofdying.com
If you are living in America there is a 1 in 615 chance that your cause of death will be the result of an automobile accident.
So yes, it is unlikely that we will ever create a tool that can answer with 100% confidence. It is also unlikely that a manufacturing process will result in a widget that conforms to allowed tolerances 100% of the time.
However, in manufacturing this is understood. A defect of 3.4 per million widgets is considered an incredibly high process capability.
These tools are being made more reliable everyday. Please have a realistic goal in mind.
Edit: Well I've learned this much. Many of you are not Beyesians!