There's no concrete way to prove my kid's imaginary friend isn't real, but that doesn't mean both sides have an equivalent likelihood and burden of proof.
If that were the only known fact about said imaginary friend on either side, then it would mean exactly that. The reason that there are different expectations of veracity are exactly because there are a bunch of priors being held about imaginary friends, by definition, not being real.
The output of the LLMs would suggest a different metaphor. The supposed divine inspiration of the Bible, perhaps?
Compare "Intelligent Design" vs. the use of genetic algorithms in AI. Simple forms of intelligence can get you a long way and can seem very impressive, especially if they have a lot of subjective experiences, which DNA gets from deep time and which AI gets from transistors outpacing synapses by the ratio to which a pack of wolves outpace continental drift.