When I spend time on something that turns out to be incorrect, I would prefer it to be because of choice I made instead of some random choice made by an LLM. Maybe the author is someone I'm interested in, maybe there's value in understanding other sides of the issue, etc. When I learn something erroneous from an LLM, all I know is that the LLM told me.
People should be able "throw the ideas away if they turn out to be wrong" but the problem is these ideas unconsciously or not help build your model of the world. Once you find out something isn't true it's hard to unpick your mental model of the world.
Intuitively, I would think the same, but a book about education research that I read and my own experience taught me that new information is surprisingly easy to unlearn. It’s probably because new information sits at the edges of your neural networks and do not yet provide a foundation for other knowledge. This will only happen if the knowledge stands the test of time (which is exactly how it should be according to Popper). If a counterexample is found, then the information can easily be discarded since it’s not foundational anyway and the brain learns the counterexample too (the brain is very good in remembering surprising things).
It's the same issue with Google Search, any web page, or, heck, any book. Fact checking gets you only so far. You need critical thinking. It's okay to "learn" wrong facts from time to time as long as you are willing to be critical and throw the ideas away if they turn out to be wrong. I think this Popperian view is much more useful than living with the idea that you can only accept information that is provably true. Life is too short to verify every fact. Most things outside programming are not even verifiable anyway. By the time that Steve Jobs would have "verified" that the iPhone was certainly a good idea to pursue, Apple might have been bankrupt. Or in the old days, by the time you have verified that there is a tiger in the bush, it has already eaten you.