I figured it out. The solution involves MergedDictionaries, but the specifics must be just right, like this:
<UserControl.Resources>
<ResourceDictionary>
<ResourceDictionary.MergedDictionaries>
<ResourceDictionary Source="ViewResources.xaml" />
</ResourceDictionary.MergedDictionaries>
<!-- This works: -->
<ControlTemplate x:Key="validationTemplate">
...
</ControlTemplate>
<style x:key="textBoxWithError" TargetType="{x:Type TextBox}">
...
</style>
...
</ResourceDictionary>
</UserControl.Resources>
That is, the local resources must be nested within the ResourceDictionary tag. So the example here is incorrect.