They would, but I think challenging facts will be easier. Instead of saying "I heard if from blah" and not having an easy way to fact check it, you just get LLMs to challenge one another. LLMs (today's, not future versions which could be drastically different) don't have a built in goal post mover.
That assumption presumes the existence of more than one model. Currently, numerous models are being developed frequently, and I hope the price decreases. However, if a single model captures 90% of the market, the others will cease to be updated, making it easier to control. What would transpire in an authoritarian country? Would they permit a disputed border to be included in that model? If that company were acquired by the first trillionaire, could they alter history to favor any wrongdoings they committed to achieve that status? Power is accumulating, not dispersing.