The rules say if you are on the point of a corner and take hits from a diagonal source, you get cover. is this an exact diagonal line only (so only a shot through multiple dots)? or is it any shot coming from an angle that can get LOS (say, one square off from true diagonal)?

it only for exact diagonals

Agreed. If the shooter is one square one way then you can't see the target and if its one square the other way the models can be easily seen, so no cover.