I think it's possible that the whisker marks are a leftover design from the original naruto from the pilot, where naruto himself was the nine-tails. The whiskers were probably always intended to be associated with the nine-tails, Keep in mind that the Ginkaku and Kinkaku also have them. If naruto didnt have the nine-tails as an adult, I'd wager Himawari and Boruto wouldn't have them. But as for lore reasons, I'd go with Ultima's idea.
Yeah Naruto only has whiskers because of Kushina being Kurama's jin when pregnant with Naruto, from conception to birth. So in a weird way Kurama is kind of like Naruto's third parent since his DNA had influence on Naruto that way..