When you use the georeferencing tool you should end up applying a transformation model to the image. When this happens, the pixels of the image are realigned to according to the model and to do this the pixel values will have to be resampled (e.g. nearest neighbor, bi-linear interp, or cubic convolution). I suspect that the precise orientation and alignment of the pixels will also be affected by your environment setting. Try setting your output coordinates. You could create an extent rectangle for your entire project area and then converting it to a simple grid and using that grid as your Snap Raster in the Output Coordinate section of your Environment Settings.