Skeptic,
That is more or less true, but there are a LOT of caveats, and the LEDs we are using are both expensive and not very tolerant.
LEDs work in such a way that they have a functional curve that describes how much current they will pull at a given voltage. A Cree XR-E might be spec'd to pull about 1A at about 3.9v, for example. So, give it exactly 3.9v all the time under all conditions and you'll be fine. However, you need a way to lock in a very tight control over that 3.9v Get the voltage a few tenths higher than it should be, and poof. A few tenths lower, and you'll have a tiny fraction of the output. And, of course, the 3.9v spec is just an average, and you might get a batch that does 1A at 3.8v, or 4.0v, so you'd have to experiment to get it right. And, you'd have to hope that your power supply had very little ripple and didn't fluctuate with temperature or load changes.
In other words, if you literally tried to hook up 4 of those 3v LEDs to a power supply labeled as 12v, you'd most surely be unhappy with the result. Hence, most people decide to use a constant-current driver, such as a puckpuck or mean well (or DIY'd.) A constant current driver basically monitors the current flowing through the LED array, and adjusts the voltage up or down as needed to keep the current at the specified value, despite changes in temperature, load, or other environmental conditions.
The LED you linked to is OK to use, it's basically a very slightly more efficient (but slightly more pricy and harder to get) version of the Q5 XR-E most people are using. Also, it's the WG color bin, while the WC color bin some vendors have is probably ever-so-slightly more desireable.