This should work:
styles.selected_style = styles["MyStyle"]
pages[0].update(2)
The API docs isn't always correct. Some times the info is lacking, some times it's confusing, some times it's plain wrong.
Page.use_style=
sets whether or not the Page (called Scenes now in SketchUp) will store the Styles. If you select your page (scene) in the Scenes toolwindow you see there is a series of checkboxes that let you save camera, hidden geometry, layers, section planes etc. This is the property you set with
Page.use_style=
For instance, select a page (scene) and make a reference to it - keep the Scenes window open and types these commands:
page.use_style = false
UI.refresh_inspectors
Notice that the "Styles and Fog" checkbox got unticked. Also note that you need to call UI.refresh_inspectors
in order for the UI to update when setting this property.