That is right. You have to consider several things about Koi
-Massive waste producers
-Will reach 30"+
-Socail fish, should be kept with other Koi
-High oxygen requirement
-Cosntantly active
All of this means they require a large body of water. Most Koi keepers will also keep their Koi outside where they are exposed to the elements and varying temperatures, which means they require a deep pond to survive and keep warm. Its this depth that gives the rise to the 1000 gallon rule. One thousand gallons is accurate for fish being kept outdoors in a group of five or more. But when the fish are inside with a constant temperature, oxygen concentration and very good filtration the rules can be bent slightly, I would give it a go but be prepared to provide a larger home as they grow, some can exceed 30" with ease.
Don't forget these fish fetch high prices so its in most Koi keepers interest to provide them with the best home, once again giving rise to the suggested 1000 galllons.