We can only guess, so that's what I'll do before this gets closed as Primarily Opinion Based. We know Robert was convinced she was kidnapped and raped by Rhaegar, he says this in A Game of Thrones
"Unspeakable?" the king roared. "What Aerys did to your brother Brandon was unspeakable. The way your lord father died, that was unspeakable. And Rhaegar … how many times do you think he raped your sister? How many hundreds of times?" His voice had grown so loud that his horse whinnied nervously beneath him. The king jerked the reins hard, quieting the animal, and pointed an angry finger at Ned. "I will kill every Targaryen I can get my hands on, until they are as dead as their dragons, and then I will piss on their graves."
A Game of Thrones - Eddard II
So we can be led to believe that Ned told Robert she'd died of his abuse or something along those lines.
Most people in Westeros though of Rhaegar as a wonderful person, the most beautiful and a lovely singer. It is unlikely they would've believed this glorious man would preform such unspeakable acts (not so unspeakable in that world). We therefore have no idea what Ned told his brothers, family or the rest of the people. Except that people assume she was kidnapped, and know she came back dead.