If it's consistently applied, any AI agent provider has to comply with cease and desist letters that tell the company to make specific false claims

The arguments of the ruling should generally apply even when the AI agent makes false statements it wasn't notified about. But in that case the defendant might have a stronger claim about not being able to reasonably ensure the correctness of all statements, and having taken reasonable measures to ensure correctness. Google couldn't really claim any of that after ignoring cease and desist letters about the false claims