I'm so glad you brought that up. This is a bugbear of mine and I've been wanting to get it off my chest for months. I've seen similar advice in numerous postings, I've seen it in BYO articles, even the odd chemistry graduate will trot it out, but it's 100% wrong. Well somewhat more than half wrong at least - bear with me. I believe proponents of chill and carb are confusing to different concepts -
solubility and
rate of dissolution.
Solubility describes what happens when the system is in equilibrium.
Rate of dissolution is concerned with kinematics; how fast the system gets to equilibrium.
Gas solubility in a liquid (or a solid for that matter) increases with a decrease in temperature, but for a given equilibrium concentration the rate of dissolution will not. Of course to achieve the same equilibrium concentration at a higher temperature you need more pressure.
For example if you want to carb a beer to 2.5vols you can apply 10psi of CO2 at 2degC, or 27psi at 20degC. The beer at room temperature will be carbed sooner than the cold beer. There's an obvious downside to carbing at room temperature, and it's the real reason that breweries carb cold - normally you've already chilled the beer before carbing and you want it cold after carbing. Warming up the beer, and then chilling it again takes time and energy.
However, there is an additional benefit to carbing before chilling. CO2 can exist in water in a number of different states. At one end of the spectrum C02 will bind relatively tightly with water to form carbonic acid. At the other end
nanobubbles are subject to viscous forces which effectively negates their flotation, but they're not chemically bound to the water at all. Counter-intuitively when people talk of carbonic bite it's not the carbonic acid in the beer that is responsible. It's the loosely bound CO2 which forms carbonic acid directly on the tongue. So, beer with a lot of loosely bound CO2 will give carbonic bite, and go flat quickly. One way to cause the CO2 to bind more tightly is to carb it warm, and then drop the temperature.
For anyone wanting to read in detail about the intricacies of carbonation I can recommend this
ebooklet by Bob Molony, a consultant chemist to the food and beverage industry.