I encountered a mysterious problem when attempting to change the parent for one of my child themes. After I made the change to the template setting in the child's style.css file the site returned the white page of death. After some debugging the error reported indicated that there was a conflict with a function in the old parent theme!
The answer is that the template is contained in wp_options in the database, so changing it in style.css had no effect if the theme was already activated. The fix is to switch to another theme before making the change and then reactivate the changed theme, or update the wp_options manually to reflect the parent theme name.
I hope this is of help to others who need to change the parent theme for a child.