Do you have to buy the PS3 version just to play your account from Windows on PS3?

My family has 4 service accounts, one for each family member. We have 3 windows accounts and one PS3 account. One of our computers died and it's going to be awhile before we can get a replacement computer. So we were going to have someone take turns on the PS3. So the PS3 has the game installed, updated, etc.

However when we go to try and log in using service account that does not have PS3 on it, but windows, it says you must first register this account for PS3. So I go into the mog station to do this and it tells me I have to buy the game again and register it through the PSN. Well I already have it, I don't need to redownload it I just want to be able to pick any of my 4 (Paid for and active) service accounts form any device that provides the service.

We were always able to do this with FFXI with XBox, PS2 and Windows, why shouldn't we be able to do this with FFXIV?

You must have a PS3 key linked to your account to play on the PS3.

Unfortunately, yes. Licenses are not portable across platforms like with XI. However, the PC license is portable from one PC/Laptop to another--just need to sign in with the proper SE AM credentials for the alternate account. So, as an alternative, you can share one of the PC/Laptops instead.