Not always true, due to the way that different states handle sales tax. Many states, for example, only charge sales tax on the difference between trade-in value and the purchase price of the new car. This sales tax savings can make a difference in such states. In Texas, this translates to 6.25%. It's therefore worth selling privately in Texas only if one can get more than a 6.25% premium over trade-in, otherwise it's better to trade it in.
You're really doing something wrong as a private seller if you can't beat 6.25% with a private sale over trade in. Car dealers don't offer 6.25% or less from what they will ask for the car.
I just private sold 2 Jaguar XFs, and the trade in values were $6K and $7K. I priced them cheap for quick sale and sold them on Craigslist ($5 listing fee per car), both in just 4 days of listing, for $10K and $11.5K. Dealers were asking closer to $15K for these cars.