Having the UVs in the opposite direction is how it's easiest to describe, but that's not actually correct either. For a trail with an "infinite" life, just having UVs start at the oldest point would "fix" it vs the existing Tile texture mode, but trails usually have a limited life span so this explanation is insufficient. More explicitly it's that the UVs are static from when the point is spawned and never changed.
This is how trails with the Tile mode currently behave in Unity.
This is how nearly everyone expects it to behave. (Ignore the shading differences, this was a quick hack.)
It's still world space tiling, but the texture "stays put" as the trail pans across the world rather than being dragged along with it.
The other things discussed above are "nice to haves" that increase the quality of trails, especially with out having to increase the poly count or modify older segments, specifically the negative color / "over UV" trick, neither of which would work with how Unity's trails and general particle shaders work.