Your problem stems from the TreeViewItem default template. A TreeViewItem element wraps any content placed in a TreeView. The TreeViewItem's template is Grid containing three columns with the width of the first two set as Auto while width of the third is set as *. The element holding the Header content is in the second column and its content alignment set to Left.
I've extracted the template for the TreeViewItem and modified it so that the content container for the header spans the second and third columns and has its content alignment set to stretch.
(This is a modified clone of the WPF template so it's a bit lengthly)
<TreeView>
<TreeView.ItemContainerStyle>
<Style TargetType="TreeViewItem">
<!-- set the headers content to stretch -->
<Setter Property="Control.HorizontalContentAlignment" Value="Stretch"/>
<Setter Property="Template">
<Setter.Value>
<ControlTemplate TargetType="TreeViewItem" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation" xmlns:s="clr-namespace:System;assembly=mscorlib" xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml">
<Grid>
<Grid.ColumnDefinitions>
<ColumnDefinition Width="Auto" MinWidth="19" />
<ColumnDefinition Width="Auto" />
<ColumnDefinition Width="*" />
</Grid.ColumnDefinitions>
<Grid.RowDefinitions>
<RowDefinition Height="Auto" />
<RowDefinition />
</Grid.RowDefinitions>
<ToggleButton IsChecked="False" ClickMode="Press" Name="Expander">
<ToggleButton.Style>
<Style TargetType="ToggleButton">
<Style.Resources>
<ResourceDictionary />
</Style.Resources>
<Setter Property="UIElement.Focusable">
<Setter.Value>
<s:Boolean>False</s:Boolean>
</Setter.Value>
</Setter>
<Setter Property="FrameworkElement.Width">
<Setter.Value>
<s:Double>16</s:Double>
</Setter.Value>
</Setter>
<Setter Property="FrameworkElement.Height">
<Setter.Value>
<s:Double>16</s:Double>
</Setter.Value>
</Setter>
<Setter Property="Control.Template">
<Setter.Value>
<ControlTemplate TargetType="ToggleButton">
<Border Padding="5,5,5,5" Background="#00FFFFFF" Width="16" Height="16">
<Path Fill="#00FFFFFF" Stroke="#FF989898" Name="ExpandPath">
<Path.Data>
<PathGeometry Figures="M0,0L0,6L6,0z" />
</Path.Data>
<Path.RenderTransform>
<RotateTransform Angle="135" CenterX="3" CenterY="3" />
</Path.RenderTransform>
</Path>
</Border>
<ControlTemplate.Triggers>
<Trigger Property="UIElement.IsMouseOver">
<Setter Property="Shape.Stroke" TargetName="ExpandPath">
<Setter.Value>
<SolidColorBrush>#FF1BBBFA</SolidColorBrush>
</Setter.Value>
</Setter>
<Setter Property="Shape.Fill" TargetName="ExpandPath">
<Setter.Value>
<SolidColorBrush>#00FFFFFF</SolidColorBrush>
</Setter.Value>
</Setter>
<Trigger.Value>
<s:Boolean>True</s:Boolean>
</Trigger.Value>
</Trigger>
<Trigger Property="ToggleButton.IsChecked">
<Setter Property="UIElement.RenderTransform" TargetName="ExpandPath">
<Setter.Value>
<RotateTransform Angle="180" CenterX="3" CenterY="3" />
</Setter.Value>
</Setter>
<Setter Property="Shape.Fill" TargetName="ExpandPath">
<Setter.Value>
<SolidColorBrush>#FF595959</SolidColorBrush>
</Setter.Value>
</Setter>
<Setter Property="Shape.Stroke" TargetName="ExpandPath">
<Setter.Value>
<SolidColorBrush>#FF262626</SolidColorBrush>
</Setter.Value>
</Setter>
<Trigger.Value>
<s:Boolean>True</s:Boolean>
</Trigger.Value>
</Trigger>
</ControlTemplate.Triggers>
</ControlTemplate>
</Setter.Value>
</Setter>
</Style>
</ToggleButton.Style>
</ToggleButton>
<!-- other problem was here set the Borders ColumnSpan to 2 -->
<Border BorderThickness="{TemplateBinding Border.BorderThickness}" Padding="{TemplateBinding Control.Padding}" BorderBrush="{TemplateBinding Border.BorderBrush}" Background="{TemplateBinding Panel.Background}" Name="Bd" SnapsToDevicePixels="True" Grid.Column="1" HorizontalAlignment="Stretch" Grid.ColumnSpan="2" >
<ContentPresenter Content="{TemplateBinding HeaderedContentControl.Header}" ContentTemplate="{TemplateBinding HeaderedContentControl.HeaderTemplate}" ContentStringFormat="{TemplateBinding HeaderedItemsControl.HeaderStringFormat}" ContentSource="Header" Name="PART_Header" HorizontalAlignment="{TemplateBinding Control.HorizontalContentAlignment}" SnapsToDevicePixels="{TemplateBinding UIElement.SnapsToDevicePixels}" />
</Border>
<ItemsPresenter Name="ItemsHost" Grid.Column="1" Grid.Row="1" Grid.ColumnSpan="2" />
</Grid>
<ControlTemplate.Triggers>
<Trigger Property="TreeViewItem.IsExpanded">
<Setter Property="UIElement.Visibility" TargetName="ItemsHost">
<Setter.Value>
<x:Static Member="Visibility.Collapsed" />
</Setter.Value>
</Setter>
<Trigger.Value>
<s:Boolean>False</s:Boolean>
</Trigger.Value>
</Trigger>
<Trigger Property="ItemsControl.HasItems">
<Setter Property="UIElement.Visibility" TargetName="Expander">
<Setter.Value>
<x:Static Member="Visibility.Hidden" />
</Setter.Value>
</Setter>
<Trigger.Value>
<s:Boolean>False</s:Boolean>
</Trigger.Value>
</Trigger>
<Trigger Property="TreeViewItem.IsSelected">
<Setter Property="Panel.Background" TargetName="Bd">
<Setter.Value>
<DynamicResource ResourceKey="{x:Static SystemColors.HighlightBrushKey}" />
</Setter.Value>
</Setter>
<Setter Property="TextElement.Foreground">
<Setter.Value>
<DynamicResource ResourceKey="{x:Static SystemColors.HighlightTextBrushKey}" />
</Setter.Value>
</Setter>
<Trigger.Value>
<s:Boolean>True</s:Boolean>
</Trigger.Value>
</Trigger>
<MultiTrigger>
<MultiTrigger.Conditions>
<Condition Property="TreeViewItem.IsSelected">
<Condition.Value>
<s:Boolean>True</s:Boolean>
</Condition.Value>
</Condition>
<Condition Property="Selector.IsSelectionActive">
<Condition.Value>
<s:Boolean>False</s:Boolean>
</Condition.Value>
</Condition>
</MultiTrigger.Conditions>
<Setter Property="Panel.Background" TargetName="Bd">
<Setter.Value>
<DynamicResource ResourceKey="{x:Static SystemColors.ControlBrushKey}" />
</Setter.Value>
</Setter>
<Setter Property="TextElement.Foreground">
<Setter.Value>
<DynamicResource ResourceKey="{x:Static SystemColors.ControlTextBrushKey}" />
</Setter.Value>
</Setter>
</MultiTrigger>
<Trigger Property="UIElement.IsEnabled">
<Setter Property="TextElement.Foreground">
<Setter.Value>
<DynamicResource ResourceKey="{x:Static SystemColors.GrayTextBrushKey}" />
</Setter.Value>
</Setter>
<Trigger.Value>
<s:Boolean>False</s:Boolean>
</Trigger.Value>
</Trigger>
</ControlTemplate.Triggers>
</ControlTemplate>
</Setter.Value>
</Setter>
</Style>
</TreeView.ItemContainerStyle>
<RichTextBox HorizontalAlignment="Stretch" HorizontalContentAlignment="Stretch">
<FlowDocument>
<Paragraph>
<Run>
Hello
</Run>
</Paragraph>
</FlowDocument>
</RichTextBox>
</TreeView>
