Yes, there is a deeper meaning behind the wide input voltage range detailed in the specifications you're working from.
In general, all electrical components, especially integrated circuits, have some specific range of voltages they operate under. Although a professional electrical engineer would have no issues designing a stable power supply with very little fluctuations in voltage, it adds complexity to the final circuit and therefore added cost to the customer. Since power supply implementations are different for each specific circuit design, it's not uncommon for a semiconductor company to manufacture the same product with different supply voltage ranges in an effort to reach the greatest number of customers (the same idea applies to operating temperatures).
Many devices have both a working voltage and an absolute minimum supply voltage. The working voltage is the voltage required for normal operation whereas the absolute minimum is the minimum voltage needed for basic functionality of the device. This concept is most prevalent when working with microcontrollers - if you supply the IC with the absolute minimum voltage, the device still turns on and operates, but disables certain services (like analog-to-digital conversions) that require a higher voltage reference. Since the device you describe is more than just an LED, I wouldn't be suprised if 6V is the minimum required for the cooling fan or regulator, but not enough for the LED to actually be powered.
Referencing your example specifically, automotive circuits and components often have their own superset of input voltage ranges and normal operating temperature conditions. That's because modern auto batteries are subject to load dump (upwards of 75V+) and cold-cranking (6V or less) conditions under heavy load, both of which alter the voltage of the battery significantly. HERE is a great paper written by Texas Instruments that explains these conditions in detail as well as some circuit examples on how to approach circuit design in automotive applications. At the very least, it should shed some light on why it's important to have wide input operating voltages.
Simply put, the component manufacturer has no indication on what their product will be used for, or from what source it will be supplied power. Therefore, in order to reach the greatest number of customers electrical components need to be able to tolerate fluctuations in supply voltage.