Stupid syntax error. I needed to set the ItemsTemplate for the Inner ItemsControl. I was setting the content of the ItemsControl to be the Rectangle.
<ItemsControl ItemsSource="{Binding Rows}">
<ItemsControl.ItemTemplate>
<DataTemplate>
<StackPanel Orientation="Horizontal">
<TextBlock Text="{Binding RowName}"/>
<ItemsControl ItemsSource="{Binding Statuses}">
<ItemsControl.ItemsPanel>
<ItemsPanelTemplate>
<StackPanel Orientation="Horizontal"/>
</ItemsPanelTemplate>
</ItemsControl.ItemsPanel>
<ItemsControl.ItemTemplate>
<DataTemplate>
<Rectangle Style="{Binding RelativeSource={RelativeSource Mode=FindAncestor, AncestorType=Grid}, Path=RectangleStyle}"/>
</DataTemplate>
</ItemsControl.ItemTemplate>
</ItemsControl>
</StackPanel>
</DataTemplate>
</ItemsControl.ItemTemplate>
</ItemsControl>