I've heard two stories about car dealers that each say different things.
One story was about a car dealer that told its salesmen the actual wholesale price of the cars they were selling. The salesmen would deal from that price upwards and would always sell the cars close to that price. They changed to only telling them the retail price of the car and then sales from that point on were much higher as the selling prices clustered nearer to retail.
But the other story was from a friend who used to work at a car dealer. The top sales guy would move an enormous number of cars. He would sell them for $250 over invoice. My friend said he was amazing, and it was common for other salesmen to spend hours haggling with a customer on one car, and meanwhile the top guy would move 4 or 5 cars.
But otherwise I agree. The company always has such a strong hand that it’s in your best interest to play every one of your cards as strategically, carefully as possible.
It does not benefit you to disclose the information, even if you think your number is high. They might assume you are lying, or they might already be anchored at an even higher number - you don't know.