Yes, I agree - but in that case they would perhaps note a slow spin (still "the same explanation").

That's just semantics tho, we are saying the same thing.
A bit like saying 'we only have one method of travel from point A to B' and additionally nothing not to use that one method to travel in the opposite direction of B (bcs then it's no longer from A to B). That is absolutely correct & a relevant note to be precise (and absolutely more relevant than the title with the "shouldn't exist").

Also, I'm not sure, but it might be exceptionally rare for the two to orbit each other with opposite spins.