I’m afraid your friend is incorrect about Rhaenys.
Q: Do you have any idea what Rhaenys and Aegon looked like? (Hair color, eye color, etc.)
A: Rhaenys looked more like a Martell, Aegon more a Targaryen.
–GRRM, August 26, 2000
Note also that when Rhaenys was presented at court, “Queen Rhaella embraced the
babe warmly, but King Aerys refused to touch or hold the
child and complained that she “smells Dornish.””
More examples of Targaryen/other relationships where the child took after the non-Targaryen parent:
(art by Douglas Wheatley for The World of Ice and Fire)
Jacaerys, Joffrey, and Lucerys Velaryon, the children of Princess Rhaenyra Targaryen’s first marriage to Laenor Velaryon. While Laenor was a Velaryon and thus of Valyrian heritage and appearance like the Targaryens, he was also well-known to prefer men; the father of Rhaenyra’s sons was almost certainly her protector Ser Harwin “Breakbones” Strong. All three boys had brown hair and eyes, and pug noses, like Strong and unlike their mother or nominal father. But note all three boys were also dragonriders, so a non-Targaryen parent does not prevent that connection.
(art by Marc Simonetti for The World of Ice and Fire)
Aegor Rivers, “Bittersteel”, the bastard son of King Aegon IV (“the Unworthy”) and his mistress Barba Bracken. Per GRRM, “Since his mother was not a Targ, he does not have the coloring. He has the purple eyes, but his hair is black.” (I could also mention another of Aegon IV’s bastards, Brynden “Bloodraven” Rivers, but since he was albino and thus looked like neither of his parents, he’s not really relevant to your question. Also Aegon IV’s three bastards by Bellegere Otherys, “the Black Pearl”, were mixed-race and almost certainly looked more like their mother.)
(art by Mike S. Miller, for the Hedge Knight graphic novel)
Baelor “Breakspear” Targaryen, son of Daeron II and the Dornish princess Mariah Martell. The Prince of Dragonstone and Hand of the King was an honorable and just man, but “too many men looked upon Baelor’s dark hair and
eyes and muttered that he was more Martell than Targaryen”. Baelor’s son Valaar also had brown hair like his father, albeit with a silver-gold streak. Also, Daeron’s grandson and namesake, Maekar’s son prince Daeron (aka “the Dreamer” or “the Drunken”) had “common hair” and could pass for non-Targaryen.
(art by Karla Ortiz for The World of Ice and Fire)
King Aegon V (“the Unlikely”) married Betha Blackwood, “known as Black Betha for her dark eyes and raven hair.” The picture above shows Aegon with his and Betha’s three sons, Duncan, Jaehaerys, and Daeron. As you can see, Duncan clearly has his mother’s coloring, Daeron’s hair is a darker silver than usual for a Targaryen, and only Jaehaerys has a fully Targaryen appearance. (Note that Jaehaerys was Rhaegar, Viserys, and Dany’s grandfather.)
Anyway, these are my thoughts: Targaryen coloring is obviously not always dominant in Targaryen/non-Targaryen relationships in both the past and within recent history. Jon Snow looks like his mother Lyanna, with the dark hair and grey eyes of the Starks. Hope that helps!