I meant that the threshold to change major or division may be higher than 2.0 (e.g. 2.5 or 3.0 or whatever). I would consider 2.0 or C grades to be essentially unrestricted (students below that probably have other issues to deal with, like academic probation or dismissal).
Some schools direct admit, some do not (or admit to a pre-nursing or pre-engineering program), and some direct admit some but require others to compete for the remaining spaces. Of course, at direct admit schools, students who initially entered for some other major may find it very difficult to change into the restricted major.