This is just my thoughts as I think about the problem. Unless you are georeferencing to a very high level of accuracy (I don't just mean zooming really far into ArcMap because even your GPS co-ordinates will have error etc), in order to fit that extra point on the co-linear line the data will be warped by a more complex algorithm that can't fit exactly through all of those points. When you only have two, it's easy to fit an algorithm to fit the raster accurately through both data points. When you add the third it will generate small residuals at each point to fit.
Something like this quick conceptual sketch - maybe could have exaggerated it a bit.
In reality the second line would be curved but it still wouldn't pass precisely through all three points.
What exactly are you georeferencing? Some control points that are not in a line would probably be a good idea. A nice big convex hull of control points and some fill is what you want.