Many sources are saying that SE has already stated buying a PS3 version of the game will allow you download the client on PS4.
These sources are absolutely wrong. I specifically remember Yoshi-P addressing that very question. Unfortunately, I've watched and read so many different interviews, I can't remember where, but I'll see if I can find it and update post. The answer is, if you want to play the PS4 version, you'll have to buy it, regardless of whether you bought the PS3 version or not. You can, however, play a character created on the PS3 version on the PS4 version, granted it was registered to the same account.
EDIT: Found the source - http://www.rpgsite.net/interviews/451-final-fantasy-xiv-a-realm-reborn-interview-with-naoki-yoshida
RPG Site: The PS4 version -- were you concerned at all that in announcing that you could gut sales of the PS3 version by causing people to wait?
Yoshida: Because we're going with a subscription model, what really matters to us is the number of subscribers - so if the player prefers to wait for the PlayStation 4 version to come out, that's fine; I don't really mind.
I think it was a bigger concern that someone might buy the PS3 version and then find out that the PS4 version was coming out right after they bought it; that would be more shocking as it might upset players. I thought it would be better to let players know up front that the PS4 version is coming out, but in the meantime you can start out playing the PS3 version if you want, as we have squeezed the maximum quality from that platform. Start with that platform if you wish and enjoy the game experience; all the character data you gain with the PS3 version can then be converted to the PS4 version.
I thought that message would be more straightforward and less confusing to players; that's the reason why we decided to make the announcement now. It's really up to the players - if they want to wait for the PS4 version, that's fine.
RE:EDIT Looking back at those links you posted, it seems to me you just misunderstood. All they are saying is that you'll be able to transition PS3 characters to the PS4 version, not that the PS4 version will be provided, free of charge. Edited, Jul 10th 2013 4:04am by DragonBourne Edited, Jul 10th 2013 4:18am by DragonBourne