Fair point--you have no idea what happens behind closed doors and what the available budgets are. And you never will. Perhaps the hiring manager decided they are willing to pay 2x the market rate because their pain is quite high. But how likely is it, due to your refusal to name a number, that the company is going to reveal the top of their range? So, yes, there is an information disparity.

But I still think that refusing to name a number shouldn't be the number one point in all of these discussions and blog posts about salary negotiation. You're right, when there are huge amounts of information disparity, either because a company's pain point is significantly higher than market rates would imply, or because a candidate has a rare and unique skill that cannot be easily found, then all of the entry-level negotiating tactics go out the window. But for fair-market jobs and candidates, I think you should be able to know your value well and refusing to name a number is a waste of time and energy.