Technically, mothers can "deny their children", actually, although it is undoubtedly much less common. Every once in a while to run into a case where there is a large family, the oldest daughter gets pregnant at a young age without being married, and the child is simply passed off as the real mother's youngest sibling. There's also such a thing as adoption.
The point is, if you match someone over 2000cM (but less than 3000cM), that person can only be a full sibling. If they were really a half-sibling, the match would only be somewhere between 1500cM and 1900cM.
For more distant relations, it's harder to tell whether it's really a half-relation instead of a full one, so seeing if you have appropriate matches on both sides of your family becomes more important. Sometimes you'll have a match that's too strong to be a half-relation, but other times you might not. The confirmation rules are not completely foolproof, I don't think, but cases that "fall between the cracks" have to be pretty uncommon. I haven't run into one, or heard about one yet.