The Important Thing To Remember Is That
Vertexes are not stored in the map file. Face planes are stored in the map file.
The editor derives the vertexes and edges by intersecting the planes in a brush.
Take a look at this:
http://i.imgur.com/Uk8xH4q.png (modo)
Imagine that's a wedge brush to begin with. Ignoring the third dimension, it is defined by the planes A, B and C. Those planes are stored by storing the coordinates of three points the plane passes through. Traditionally, these three coordinates have to be integers. The two dots on each "plane" in my drawing show suitable coordinates for this. (Again, ignoring the third dimension here.)
Now if we clip that brush using the plane D, we are simply adding plane D to the brush definition. The coordinates for this plane is also easily stored using integers.
HOWEVER, one of the new vertexes that the brush gets, circled in red, is definitely NOT on grid. Its coordinates would be 2/3'ds of something.
The brush is still perfectly valid and "on grid" in a sense, even if its vertexes isn't.
SPoG wrote a really excellent document about the technicalities of the MAP/BSP format a while ago. It was hosted on PQ but then that died, so I rehosted it but then spawnpoint.org died, so now I have no clue where on might find this again.
If someone has it, please link it here because it is essential reading imho.