In an (infinite) hexagonal grid, every hex got 6 adjacent vertices and every vertex is shared by 3 adjacent hexes. That means that if you want each vertex to "belong" to one and only one hex, then each hex would have to "own" two vertices. That way every vertex would have an "owner". Which two vertices? That's up to you. If you choose the same two vertices of each hex, then you will notice that every vertex now clearly belongs to a hex.
Except, of course, if you have a finite grid. Then you would have vertices at the border which would need to be owned by a "virtual" hex that's outside of the grid. But that's a problem you have with rectangular tiles as well.