The past never dies

Like George very obviously wants people to think of Rhaegar as a good person and think of Rhaegar/Lyanna as as a tragic doomed couple but won't try to make Rhaegar actually DO things that would make the audience feel sympathetic towards him.

Possibility 1 > Ned Dayne and Allyria got the classic ethnic kid treatment of not being told important family gossip and having to piece together info from context clues and coming to the wrong conclusion

AND Ned is the lord of starfall so we know at least his Dayne parent (who would have known what actually happened) is dead. Possibly the non-dayne parent is also dead or refuses to reveal that Brandon was really the father of Asharas kid. Him and Allyria may have worked out this incorrect info and now theres no one around who can or will tell them the truth.

Possibility 2 > Allyria was probably old enough to remember Ned being in starfall when he returned Dawn but was still a small kid and just assumed that the Stark that was in their castle was the one who impregnated her older sister.

Possibility 3 > Ned Stark asked the Daynes to claim that he fathered Jon to protect him and they were like ok whatever the wars over + you bought back Dawn so we'll do you a solid and they just dont give af to correct the rumors anymore since the North is 9 gajillion miles away and they are Dornish. Ned Dayne and Allyria are told the fake rumor but never the real one and so they go around accidentally spreading misinformation

This + him ragebaiting Rhaegar and calling him a pussy and giving Robert that bottle of watery splinters