My knowledge may be a bit dated here, so maybe someone else can clarify or update.
Lets start with the stuff you already know,
LEDs or Light-Emitting-Diodes are simply Diodes (think of it as a one way valve, electricity can only flow across the diode in only one direction) that emit light when a voltage is applied. This works by converting the electical energy to light energy over a "voltage-drop" *Most*, certainly older technology diodes typically fry when the voltage-drop across the diode is greater than 3.5 volts (this varies).
Basically, the diode is asked to convert too much electrical energy to light too quickly.
To remedy this, frequently a limiting resistor would be placed in series to the diode to keep the diode within a specific range and bring the voltage at the input of the LED low enough. This is one possible solution that these superbright leds may have taken to make it work on 12v.
So, these superbright LEDs work by a) being able to handle a larger voltage drop, and b) subsequntly converting more electrical energy to light for the same voltage.
So in a nutshell, the LEDs themselves are likely not plugged directly into your 12v harness. (you plug the whole unit in, yes, but a LED as a component). The unit you buy also contains inside, some voltage regulation equipment to keep the LEDs from burning up and allow them to work on your 12v harness. But in theory, if the resistors were resistive enough, you could build a unit that plugged into your wall socket.
I hope this cleared this up instead of making things more complicated
