Not entirely true as you can set the matchmaking to private and play the game solo. (just like Elite)
You can do everything solo except the strongholds (something akin to party dungeons in MMOs) - you need to have four javelins to enter. And there is also the difficulty, of course. I have been able to do everything solo on Normal difficulty, but you don't get much good gear, that way (I only got a couple of blue and one purple gear on normal, while in full party on Hard the epics are literally raining down on you)
Naturally, it's nothing like a proper "story mode" singleplayer. But if your main concern is that other players will spoil your story missions, you CAN do them alone (and honestly it really is better that way.)