LLMs may generate false statements, but this stems from their primary function - to conjure plausible language, not factual statements. Therefore, it should not be regarded as a mistake when it accomplishes what it was designed to do.
In other words, the tool functions as intended. The user, being forewarned of the tool's capabilities, holds an expectation that the tool will perform tasks it was not designed to do. This leaves the user dissatisfied. The fault lies with the user, yet their refusal to accept this leads them to cast blame on the tool.
In the words of a well-known adage - a poor craftsman blames his tools.