In 2008, Points are kind of like "blocks".
When you insert a point, the overall "Point block" goes on a layer. This is either the current layer, or it may be the layer specified in the DescKey (if one applies, and you have DescKey matching turned on).
The Point marker and the Point label can be placed on different layers in the Point Style, but neither one affects the layer that the overall "point block" goes on. Unfortunately, the only way to control this is by setting up DescKeys, or by making sure you select the layer you want and set it current prior to creating the points.
After that, the best way to change the layer of points is to put them into a point group, and then do "Edit points" on the points group, and change the layer of all the points in the group at once.