Ws2811 is a 5V chip and using things like resistors and regulators allow it to run in a higher voltage. Given many resistor pixels have too high resistors in them, they are already under-driving the LEDs.
You can never over drive the LED as the 2811 chip is designed to limit the current through to 16mA per colour, which is about half to 2/3 of a typical 20-30mA LED.
The 78L05 regulator in regulated pixels ruins from anywhere between 7 to 30V. Noting that the higher the input voltage, the more heat it needs to dissipate.
Running a 12V system, there is loads more leniency in the input voltage range.
5V would be more picky, as the chips can get damaged due to no voltage dropping components.
Brightness doesn't come into play.
Dimming is done with PWM, being switched on and off 2000 times a second, with the on time being varied.
So at 30%, the LED is hard 100% for 0.15ms, then off for 0.35ms, and the cycle repeats.
Instantaneous current is actually 100%, but average is only 30%.
That being said, the driver chip sees power all the time, whether the LED is on, off, or dimmed.
Overall, I wouldn't be getting fussed running between 11 and 13V on a 12V system. Running slightly higher does allow you to ensure more voltage drop before issues, meaning a bit of a longer run or more pixels.
Just to add to what everyone else had said, if you add a run of pixels, or a load of some sort, and check the voltage with the load, set the voltage then.