Yes, that's true. The CO would kill them though. CO2 would not be present in enough concentration to kill anyone till long after they were dead from the CO.
Hmm..
U.S. Environmental Protection Agency
estimates of average passenger car emissions in the United States for July 2000
Component Emission Rate Annual pollution emitted
Hydrocarbons 2.80 grams/mile (1.75 g/Km) 77.1 pounds (35.0 kg)
Carbon monoxide 0.74 oz/mile (13.06 g/Km) 575 pounds (261 kg)
NO
x 1.39 grams/mile (0.87 g/Km) 38.2 pounds (17.3 kg)
Carbon dioxide 14.7 oz/mile (258 g/km) 11,450 pounds (5,190 kg)
Roughly twice as much CO2 as CO is produced.
Minimum CO level capable of causing mortality is 0.16%
Minimum CO2 level capable of causing mortality is 9.8%
So, you are correct. The CO would get you first.