That's a bold statement. How do you explain the rest of the connections besides aqua to kairi. How about Terra to Riku and Ven to Sora? They each mean similar things or parts of a whole category. In my opinion they are all connected in certain ways, of which I don't want to go through right now, but if they have nothing to do with Kairi, Riku, and Sora what is their purpose.
You do realize that you are only picking the easy pairings, don't you? Kairi is pretty much a secondary character in KH. Hate me if you must, but it's true. A major theme of KH up until now has revolved around Riku and Sora's relationshp. Terra and Ven have been getting the most speculation, making most people theorize about their relationship to Sora and Riku. Any informaiton about Aqua we have right now is pretty vague. There has been no hint, in game or otherwise, that there are any connections between these two female characters in relations to the story.
Cases differ depending on how you look at it. It's mearly a matter choosing a certain case and stating your opiniion. I mearly presented my arguement for the case of Aqua and Kairi, saying that there won't be a relation between them in the game's context. You can't just assume that the six of them have some type of conection to onr another.
Here are a couple examples: if you go by L.S.'s dialog in FM+, you could determine that Terra has a connection to Riku because he choose him, not Sora, to weild a Keyblade. Like wise, one could argue that there is a connection between Sora and Ven because Ven is identical to Roxas, Sora's Nobody, While another could argue that other than appearance, there is no relation(Please remember, I'm talking about in context of the game only. Names don't matter in context to the game until we hear Sora say "Hey! your name means the same thing as mine!" To Ven)
Now, try to find a connection between Riku and Ven. Or Sora and Aqua. Or Riku and Aqua. These match ups are harder, since there aren't any direct similarities. Even if you would make a connection, it would probably be very abstract and unbelievable,ending in it being dismissed quickly.
I'm not saying that there aren't any connections between these characters. I'm saying I think that some of them are connected while others aren't until information has been brought forth to prove otherwise. If I have ever indicated that I think that all these characters are unrelated, then I apoligize. But I plan on standing by what I said until said information is revealed.