I've created this template, which uses a style applied to the ContentPresenter so that I can bind the data object's Column property to Grid.Column, allowing the items to determine for themselves which column of the Grid they go into:

<DataTemplate DataType="{x:Type local:MyObject}">
  <ItemsControl ItemsSource="{Binding Items}">
    <ItemsControl.Resources>
      <Style TargetType="{x:Type ContentPresenter}">
        <Setter Property="Grid.Column"
                Value="{Binding Column}" />
      </Style>
    </ItemsControl.Resources>
    <ItemsControl.ItemsPanel>
      <ItemsPanelTemplate>
        <Grid>
          <Grid.ColumnDefinitions>
            <ColumnDefinition Width="*" />
            <ColumnDefinition Width="*" />
            <ColumnDefinition Width="*" />
          </Grid.ColumnDefinitions>
        </Grid>
      </ItemsPanelTemplate>
    </ItemsControl.ItemsPanel>
  </ItemsControl>
</DataTemplate>

When I run the program, I get a NullReferenceException. The beginning of the hilariously long stack trace:

at System.Windows.StyleHelper.ApplyAutoAliasRules(OptimizedTemplateContent optimizedTemplateContent, HybridDictionary childIndexFromChildID, FrameworkTemplate frameworkTemplate, FrugalStructList`1& childRecordFromChildIndex, FrugalStructList`1& triggerSourceRecordFromChildIndex, FrugalStructList`1& resourceDependents, HybridDictionary& dataTriggerRecordFromBinding, Boolean& hasInstanceValues)
at System.Windows.StyleHelper.ProcessTemplateContent(FrameworkTemplate frameworkTemplate, FrugalStructList`1& childRecordFromChildIndex, FrugalStructList`1& triggerSourceRecordFromChildIndex, FrugalStructList`1& resourceDependents, ItemStructList`1& eventDependents, HybridDictionary& dataTriggerRecordFromBinding, HybridDictionary childIndexFromChildID, Boolean& hasInstanceValues)
at System.Windows.StyleHelper.SealTemplate(FrameworkTemplate frameworkTemplate, Boolean& isSealed, FrameworkElementFactory templateRoot, TriggerCollection triggers, ResourceDictionary resources, HybridDictionary childIndexFromChildID, FrugalStructList`1& childRecordFromChildIndex, FrugalStructList`1& triggerSourceRecordFromChildIndex, FrugalStructList`1& containerDependents, FrugalStructList`1& resourceDependents, ItemStructList`1& eventDependents, HybridDictionary& triggerActions, HybridDictionary& dataTriggerRecordFromBinding, Boolean& hasInstanceValues, EventHandlersStore& eventHandlersStore)
at System.Windows.FrameworkTemplate.Seal()
at System.Windows.StyleHelper.UpdateTemplateCache(FrameworkElement fe, FrameworkTemplate oldTemplate, FrameworkTemplate newTemplate, DependencyProperty templateProperty)
at System.Windows.Controls.ContentPresenter.OnTemplateChanged(DependencyObject d, DependencyPropertyChangedEventArgs e)
at System.Windows.DependencyObject.OnPropertyChanged(DependencyPropertyChangedEventArgs e)
at System.Windows.FrameworkElement.OnPropertyChanged(DependencyPropertyChangedEventArgs e)
at System.Windows.DependencyObject.NotifyPropertyChange(DependencyPropertyChangedEventArgs args)

...etc.

It's not the binding. I still get the error if I explicitly set the value in the style's setter to 0, say. And the error vanishes if I remove the style, though then all of the items end up in column 0.

What's going on here? And how do I debug a problem like this?