You were correct in that a nautical mile is based on latitude. But I think you've got longitude on your mind? Longitudinal lines travel N/S, latitudinal lines travel E/W. Lat lines are like rungs of a ladder - the shape of the ladder can change from top to bottom (wide at the bottom, narrow at the top), but the distance between the rungs doesn't change.So, a nautical mile at the North and South poles is zero in length??
I seem to remember it is consistently one minute at the equator. But, It's been years, like 40, since the schooling....
However, at the equator, longitudinal lines are ALSO spaced such that a degree equals about 60 N miles... and a second would then be 1 mile. I bet that's what you're thinking of?