From the X-COM: UFO Defense manual, it states that X-COM is a "multi-national" covert organization, and that they were "equipped with the world's finest pilots, soldiers, scientists, engineers, working together as one multi-national force". Remember that this is an international initiative, all nations are involved, as the aliens are a global threat.
Of course XCF, changes that slightly, by beginning small, but it eventually reaches what the manual describes.
Now for the matter of agent/soldier stats and abilities, well they would obviously have "the best of the best of the best", but in-game ..? I think it's just for game balance, it helps with the feeling of beginning small and gaining experience alongside your agents/soldiers, and also makes the player feel vulnerable against threats.
After all this game is meant to be challenging but fair, if you train your recruits and make sure they survive, then they'll (eventually) become the best.