Hello Ian
Your description is correct. Think of a sub-analysis as a child of the Analysis or Parent. It is a duplicate and tends to be used for charts. So when you make a change to the crosstab of the "parent" Analysis, the "child" sub-analysis (typically a chart) also changes automatically to show the same data.
However there is just one more step to do what you want.
Create the sub-analysis.
Click on the sub-analysis to select it.
In the Display tab click on the "unlink" button.
The sub-analysis now becomes a regular Analysis and you can now do whatever you want with it.
Hope this helps.
Regards
Ian