If there is only one tile in a group and its Visibility property is set to Collapsed, the group header does not disappear.
This behavior is expected and can be reproduced with any other control with groups with items. For example ListBox with groups will leave its Group's Header even when all of its children are collapsed. If a user wants to hide the group, he/she should work with the Items collection and add/remove items from it. For example: this.tileList.Groups[1].Items.RemoveAt(0); where there is only one item. The group will not be rendered as it does not have any items.