Another hint towards Jon's true parentage and potential legitimacy is the presence of the Kingsguard at the Tower of Joy. The Kingsguard are sworn to protect the royal family at all cost. But why were three of them still at the Tower of Joy when Ned, Howland Reed, and the others showed up? By then, Rhaegar Targaryen had been killed at the Trident, which should have meant that Viserys, his younger brother, was now the heir to the throne.
Ned's party didn't ride for the Tower of Joy until they lifted the Siege of Storm's End and after the sack of King's Landing, both of which happened after the Battle of the Trident, so there would have been plenty of time for Arthur Dayne and his two companions to learn of the death of Aerys, Rhaegar, and Rhaegar's children, and leave to go and protect Viserys. But they didn't. So, to me, that implies that Rhaegar and Lyanna did marry, and Lyanna was pregnant with Rhaegar's only surviving child, who would be the legitimate heir to the Iron Throne.