If you approach this problem programmatically then there is a GOTCHA as the visible property of a style refers to whether or not a style is hidden or not hidden in the style pane. Thus visible = true actually HIDES the style because it really means Hidden = true.

My styles are not hidden.

Even when you restrict the Styles visible in the style pane you may see styles that are similar to yours but which you did not define. This means that you have used a style but in applying it have made a slight change somewhere in the paragraph. You can't delete these styles without losing the effect in the paragraph but you can hide them from being seen in the style pane by switching off the check boxes Paragraph, font and/or bullet and numbering in the Style Pane options checkbox.

The visibility property of a style has no bearing on whether text with the style applied is visible or not visible a document. The only way to do this is to use the font 'Hidden' property which is completely separate from the style visibility property.

Totally irelevant to this problem

You haven't answered anything. Just crested your own questions to answer.