sure... take the earlier example of getting a written cash offer from carmax for 10000. they ACTUALLY valued your car at 11000 but they HOLD 1000 from you to cover their fixed costs. they had market information telling them that the true value of your car is 11000, but when they hit "send" on their computers, their internal system deducts 1000.
If you take your car anywhere else for evaluation, their systems won't deduct that 1000, so if a dealer is honestly evaluating the value of your car, they will use the same market data available to carmax and should evaluate it at 11000. so, the dealer you are working with right now is offering to buy your 11000 car for 9400. pretty good deal for him.
that is why you see a lot of places now advertising (like henna chevrolet in austin) that they will offer $500 more than carmax because they know they are still coming out $500 ahead.