Is a cigarette lighter battery voltage meter accurate?
A car cigarette lighter or 12V power outlet in a car is, like most everything else, connected directly to the battery positive/alternator output, through a fuse (typically 10 Amp). Sometimes it is connected through the main switched power relay. In any case, aside from the negligible voltage drop across the fuse and wiring, is an accurate measuring point for the voltage in the car. As mentioned, 13.7 is a typical voltage for a car under load while the alternator is running.

As to the accuracy though, keep in mind that the trinket you got is a cheaply made mass produced item. It will have a resistor divider to bring the voltage down to the microcontroller voltage level. But the lower the quality of the item, the more likely that the resistor is not a very precise, and the Analog to Digital converter in the microcontroller they used will not be very accurate. For the most part, this may mean it's off by a fraction of a volt. Not precision laboratory grade. But good enough for your average user. 

Sidenote, I use one in my car due to alternator issues and it's as accurate as my free harbor freight multimeter.