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; an English release rewrote them as relatives and changed nothing on screen.
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, they are domestic together, 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 licence had moved on from DiC to Cloverway, and it was applied to the script alone.
That last detail is the one worth sitting with. Nothing was altered in the animation: the intimacy, the framing, the way the show shoots the two of them together all survived intact under dialogue insisting they were relatives. The result is not a sanitised 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 or a number that got misheard under time pressure. It is a deliberate rewrite of what two characters are to each other, made to avoid depicting a relationship, and it took a good deal of work to maintain across a whole season.
It was fixed
Viz licensed the series and produced a new English dub from 2014, restoring the original names and the original relationship along with the scenes that had been cut around it. So the current official English version says exactly what the Japanese says, and the cousins version is a historical artefact 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.