How can make ScrollViewer scroll when mouse is over *any* content - wpf

Question

The reason I stress 'any' is because CanContentScroll is not fully working in my ScollViewer.
Let me explain the scenario:
I have a ScrollViewer that has three Labels followed by a ListBox each. The reason I have this content inside the ScrollViewer is because I don't want each ListBox to have a ScrollBar, I just want one "global" ScrollBar. The problem is that when the cursor is over the the ListBox the ScrollViewer doesn't scroll. I've tried to set CanContentScroll property to true in the ScrollViewer, the ListBox and on the ListBoxItem style, without success. Is there other Control type I should use?
Here is my code sample:
<UserControl x:Class="Telbit.TeStudio.View.Controls.TestStepsView"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
xmlns:my="clr-namespace:Telbit.TeStudio.View.Controls">
<UserControl.Resources>
<DataTemplate DataType="{x:Type my:TestStepsStepViewModel}">
<my:TestStepsStepView HorizontalAlignment="Stretch"/>
</DataTemplate>
<Style x:Key="StepItemStyle" TargetType="{x:Type ListBoxItem}">
<Setter Property="SnapsToDevicePixels" Value="true"/>
<Setter Property="OverridesDefaultStyle" Value="true"/>
<Setter Property="IsSelected" Value="{Binding Mode=TwoWay, Path=IsSelected}"/>
<Setter Property="ScrollViewer.CanContentScroll" Value="True"/>
<Setter Property="Template">
<Setter.Value>
<ControlTemplate TargetType="ListBoxItem">
<Border Name="Border" SnapsToDevicePixels="true" Background="Transparent" BorderThickness="0" Padding="1">
<ContentPresenter/>
</Border>
<ControlTemplate.Triggers>
<Trigger Property="IsSelected" Value="true">
<Setter TargetName="Border" Property="Background" Value="#40a0f5ff"/>
</Trigger>
<Trigger Property="IsKeyboardFocusWithin" Value="True">
<Setter Property="IsSelected" Value="True" />
</Trigger>
</ControlTemplate.Triggers>
</ControlTemplate>
</Setter.Value>
</Setter>
</Style>
</UserControl.Resources>
<UserControl.Background>
<LinearGradientBrush EndPoint="0.5,1" StartPoint="0.5,0">
<GradientStop Color="#FFF2F2F2"/>
<GradientStop Color="Gainsboro" Offset="1"/>
</LinearGradientBrush>
</UserControl.Background>
<Grid>
<Grid.RowDefinitions>
<RowDefinition Height="30"/>
<RowDefinition Height="*"/>
</Grid.RowDefinitions>
<HeaderedContentControl Grid.Row="0" >
<HeaderedContentControl.Header>
<Grid Background="#e8f2f8">
<Grid.ColumnDefinitions>
<ColumnDefinition Width="30"/>
<ColumnDefinition MinWidth="200" Width="*" />
<ColumnDefinition Width="75"/>
<ColumnDefinition Width="60"/>
<ColumnDefinition Width="60"/>
<ColumnDefinition Width="60"/>
<ColumnDefinition Width="60"/>
<ColumnDefinition Width="120"/>
<ColumnDefinition Width="130"/>
</Grid.ColumnDefinitions>
<Label Grid.Column="0" Content="#" BorderBrush="#70add4" BorderThickness="2 2 0 2"/>
<Label Grid.Column="1"
Content="Folder\Name"
BorderBrush="#70add4" BorderThickness="0 2 0 2"/>
<Label Grid.Column="2" Content="Type" BorderBrush="#70add4" BorderThickness="0 2 0 2" Margin="-20 0 0 0"/>
<Label Grid.Column="3" Content="Auto Start" BorderBrush="#70add4" BorderThickness="0 2 0 2" Margin="-20 0 0 0"/>
<Label Grid.Column="4" Content="Run After" BorderBrush="#70add4" BorderThickness="0 2 0 2" Margin="-20 0 0 0"/>
<Label Grid.Column="5" Content="Stop After" BorderBrush="#70add4" BorderThickness="0 2 0 2" Margin="-20 0 0 0"/>
<Label Grid.Column="6" Content="Delay (s)" BorderBrush="#70add4" BorderThickness="0 2 0 2" Margin="-20 0 0 0"/>
<Label Grid.Column="7" Content="Timestamp" BorderBrush="#70add4" BorderThickness="0 2 0 2" Margin="-20 0 0 0"/>
<Label Grid.Column="8" Content="Edited by" BorderBrush="#70add4" BorderThickness="0 2 2 2" Margin="-20 0 0 0"/>
</Grid>
</HeaderedContentControl.Header>
</HeaderedContentControl>
<ScrollViewer VerticalScrollBarVisibility="Auto" Grid.Row="1" VerticalAlignment="Top" CanContentScroll="True">
<Grid>
<Grid.RowDefinitions>
<RowDefinition Height="30"/>
<RowDefinition Height="3*"/>
<RowDefinition Height="30"/>
<RowDefinition Height="3*"/>
<RowDefinition Height="30"/>
<RowDefinition Height="3*"/>
</Grid.RowDefinitions>
<Label Name="lblSetup" Grid.Row="0"
VerticalContentAlignment="Center"
BorderBrush="DarkGray" BorderThickness="0 0 0 1"
TextBlock.FontSize="10pt" TextBlock.FontWeight="Bold" TextBlock.Foreground="#949494"
Content="Setup" AllowDrop="True"/>
<ListBox Name="itmCtrlSetupSteps" Grid.Row="1"
BorderThickness="0" Background="Transparent"
ItemsSource="{Binding SetupSteps}" SelectionMode="Single"
HorizontalContentAlignment="Stretch"
ItemContainerStyle="{StaticResource StepItemStyle}"
SelectionChanged="manageStep_SelectionChanged"
ScrollViewer.CanContentScroll="True"
/>
<Label Name="lblTest" Grid.Row="2"
VerticalContentAlignment="Center"
BorderBrush="DarkGray" BorderThickness="0 0 0 1"
TextBlock.FontSize="10pt" TextBlock.FontWeight="Bold" TextBlock.Foreground="#949494"
Content="Test" AllowDrop="True"/>
<ListBox Name="itmCtrlTestSteps" Grid.Row="3"
BorderThickness="0" Background="Transparent"
ItemsSource="{Binding TestSteps}" SelectionMode="Single"
HorizontalContentAlignment="Stretch"
ItemContainerStyle="{StaticResource StepItemStyle}"
SelectionChanged="manageStep_SelectionChanged"
/>
<Label Name="lblTearDown" Grid.Row="4"
VerticalContentAlignment="Center"
BorderBrush="DarkGray" BorderThickness="0 0 0 1"
TextBlock.FontSize="10pt" TextBlock.FontWeight="Bold" TextBlock.Foreground="#949494"
Content="Tear Down" AllowDrop="True"/>
<ListBox Name="itmCtrlTearDownSteps" Grid.Row="5"
BorderThickness="0" Background="Transparent"
ItemsSource="{Binding TearDownSteps}" SelectionMode="Single"
HorizontalContentAlignment="Stretch"
ItemContainerStyle="{StaticResource StepItemStyle}"
SelectionChanged="manageStep_SelectionChanged"
/>
</Grid>
</ScrollViewer>
</Grid>
</UserControl>

Answer 1

The problem is that even though child list boxen don't have scroll bars visible, they do have ScrollViewer in them according to their template. Fortunately this template is easily modifiable. Do this for each child list box, or better yet put it in common style:
<ListBox.Template>
<ControlTemplate TargetType="ListBox">
<Border BorderBrush="{TemplateBinding BorderBrush}" BorderThickness="{TemplateBinding BorderBrush}">
<ItemsPresenter/>
</Border>
</ControlTemplate>
</ListBox.Template>
The default is almost the same with the exception of ScrollViewer wrapping around ItemsPresenter.