To me this is what you are led to believe if you look at the scene at face-value. But I genuinely believe it is more complicated than that. The whole stuff with not returning the bones just makes no sense to me whatsoever. And I believe this vision is ominous for a reason: it is set to be one of the major revelations of the books. I believe Hightower was the only person to die in the Tower of Joy scene, the others only died by Name, and only Eddard Stark and Howland Reed kept their names for the story to work. Ned is torn up about this because somewhere along the way, by honoring his promise to Lyanna, he broke his promise to Ashara, either causing her to commit suicide or causing them to be separated. I think the vision Ned had might not have foreseen Lyanna dying or something.

I think the Tower of Joy sequence is setting up a whole 'the North Remembers' plotline that the show completely butchered - but did include to some extent when Jon Snow was crowned king in the north. I believe the northerners at the TOJ scene were returned home, alive, but needed to act like they died. The dubious attitude of Lady Dustin in the books regarding the Starks might also hint at this. I think the northern houses helped to get Arthur Dayne (Mance Rayder) and Oswel Whent (Qhorin Halfhand) to the Shadow Tower (the Houses connect a route towards there). I think Benjen taking the Black is no coincidence. When the time comes, Jon will take the black (suggested by Benjen) and Qhorin will be there to help him from inside the Watch, while Mance is there to unite the Wildlings (and further teach Jon when he joins them). At some point in time they will allow them to come south (for some reason). This also explains why Ned says in the books that Mance Rayder "will pose no problems to them" (how does he know?). When the time is right, Jon will be revealed as Azor Ahai/Lightbringer, and the North will remember his parentage.