The problem is that we have no ability to conclusively determine whether or not an asteroid is on a near-collision course, or on an actually-collision course.

The problem is that we have no ability to conclusively determine whether or not an asteroid is on a near-collision course, or on an actually-collision course. And if it's the former, giving it a small bump is just as likely to put it on an actually-collision course as not doing anything at all.