There are some false and misleading information in your tutorial. When explaining AO maps you show shadows from direct lighting (sun) which is no ambient occlusion at all. Your AO map is probably not normalized, that's why it's mid grey rather than white with some darker spots (which would work just fine for multiply blend…
If you bake out an AO map correctly (normalized) it will be mostly white with darker (black) shadows. To use this texture you simply multiply it on top of the other textures. It works the same for in Photoshop and UDK, just set the layer to multiply or use a multiply node. With a working AO-map you should not need to…