Did the Sailor Moon Dub Really Say Uranus and Neptune Were Cousins?
Yes, and the Japanese never did. Haruka and Michiru are a couple in the original; the Cloverway-era English dub rewrote them as cousins, yet several episodes kept their flirting.
Yes, the English version said it, repeatedly. The Japanese never did, and the difference is not a translation problem.
What the original has
Haruka Tenoh and Michiru Kaioh, Sailor Uranus and Sailor Neptune, are introduced in the third season as a couple. It is not a subtext or a fan reading. They flirt, and the show treats the relationship as an established fact about who they are rather than as a question it intends to answer later.
What the English release did
Renamed them Amara and Michelle and rewrote them as cousins. The change arrived with the third season's English version, produced after the license had moved on from DiC to Cloverway.
The rewrite was also incomplete. Several episodes of that dub kept a noticeable amount of the two characters' casual flirting, whether to stay closer to the Japanese or through inconsistent editing, under dialogue insisting they were relatives. The result is not a sanitized version of the relationship. It is the same relationship with a caption claiming the two people in it are family, which is a stranger and less comfortable thing than what it replaced.
Why this is not the same as a mistranslation
Elsewhere on this site we deal with lines that exist only in English because a dub script invented them: Goku's "hope of the universe" speech, Vegeta's "over 9000". Those are writing choices, and arguing about them is arguing about tone.
This one is a different category. It is not a line that drifted. It is a deliberate rewrite of what two characters are to each other, made to avoid depicting a relationship.
It was fixed
Viz Media acquired the series in 2014 and had it re-dubbed, and the redub restored deleted scenes and kept to the original Japanese scripts. So the current official English version follows the Japanese, and the cousins version is a historical artifact rather than a live claim about the show.
Which makes this a useful thing to know when someone tells you what a character "said" in an anime. The honest answer is often another question: in which version, and in which decade.