You can catch the red Gyarados, it like all other Pokemon considered 'wild' are able to be captured although with certain needs of types of pokeballs and low hp and inflicted status conditions. You most likely misunderstood the spoken text (I had to re-face the elite four just so i could re-read their text was to excited). SO basically if it says "a wild (insert pokemons name here) appeared!" means you can ATTEMPT to capture the said Pokemon.
He appears after you catch/kill the red gyarados
You can catch red Gyarados anywhere because red Gyarados are only shiny but are extremely rare.
same chance to catch a shiny gyarados to catch eny shiny in platinum.
they dont have a red gyrados
To get a red Gyarados in Pokemon LeafGreen you first need to catch a shiny Magikarp. This shiny Magikarp will be able to evolve into a red Gyarados. This is due to the red Gyarados simply being the shiny color of Gyarados.
after you beat or catch the red gyarados he will drop a red scale
train it
You have to catch or defeat the red GYARADOS
you cant
In Pokemon Crystal version, you catch it at the Lake of Rage.
you are only able to catch red gyarados in Silver/Gold versions in Lake of Rage or something like that, my point is you can't catch it in Leaf Green/Fire Red
You have to go to the Lake of Rage. In the middle of the lake, there is a red gyarados. This is your only chance to catch the Red gyarados, so save before battling it to have multiple chances to catch it.