Hmm... it seems to me that the issue comes from the fact that the Point Marker references the 0 layer, meaning the parent object's layer, unlike all the other components of the alignment labels... or does it? Is the Point Marker Style referencing a different layer perhaps, one not related to the alignments, which is why it's still on?
Either way, what about:
1) placing the offending alignment on its on layer? Does that cause problems? Does the point marker come with it in the plot?
OR
2) creating a new Point Label that looks the same but that references a different layer that can be shut off in this view and applying that to the Label Properties of those two labels? I know you can do this in 2007, can't remember about 2006.
Let me know how that goes.
HTH,
Trevor