You can't do split screen because you have to be logged into the server to access your character and the same console cannot be logged on to two different accounts at the same time.

That's not necessarily the case. Borderlands allowed to split screen and the use of two separate accounts with online play. It does this by allowing you to select which PlayStation user you want to use when you select the second player. I am not advocating split screen just expressing that it could be possible.

The other players could not get to their character because the characters are locked to their psn and on Bungie's server.

So, Destiny is not set up to select a second player guardian. Let me try to make the Borderlands comparison a little clearer and put it in terms of Destiny. In Borderlands P1 character is based on the logged in local PlayStation user which is linked to a PSNID. P2 can then join and select a different local PlayStation user linked to a separate PSNID. In the case of Destiny, that would mean an entirely separate Bungie account with that user's unique guardians. For this reason I doubt there is a technical limitation based on account selection preventing Bungie from implementing split screen.

Just try logging in 2 accounts on your PlayStation and see how it goes.