What is the damage as a result of the accident? What was the accident? Will the work done to the vehicle show up on record, such as carfax? I personally can't make any observations without knowing facts. I can assume the rear bumper was replaced after somebody bumped into you.
Is the title clean, or is it salvaged?
Many of the vehicles are sold off to auction these days....it's quite common. I traded a very nice vehicle for my Canyon. The sales guy said to me "Are you sure you have everything out of the truck, it is going on the trailer in the morning to auction".
On trade, a dealer will offer you low. That is their job. You should understand the trade value of the vehicle going into the sale. And know what you are okay accepting to make a deal. If the trade offer isn't close to what you want, and you feel you can better that on private sale then no need to trade. A trade isn't something you should be concerned with aside from the money they offer you. Doesn't matter if they sell it, give it to the sales person's kid or sell it for action. Your purpose is take the money they offer you and enjoy. :) Value is something you work out at sale time....if you choose not to take the trade, leave one of the vehicles there (if you purchase the new one) and retrieve it at a later time if you are going at this yourself.
There are certain things you need to disclaim on a sale, I do not know if accident damage is included. For example, I think you need to specify if you change the engine from original (I'm not 100% on that either).
I personally am not familiar with the NADA values so I can't really speak to that.