According toIt is my opinion that code in the game meant to prevent piracy (sharing) is working as intended. That each purchase of ED is allowed one account to access Horizons, all alts will have to purchase Horizons separately. That if you purchased a pre-owned physical copy say from game stop, amazon, ebay etc, you are not the original owner, and when you registered it with Frontier they know this. Why we were giving access to Horizons in the first place was probably caused when the dlc was rolled into the game.
Both Elite Dangerous and the Horizons expansion can be shared between all PSN accounts on the console that you've set as your Primary PlayStation®4.