In WPF, why doesn't TemplateBinding work where Binding does?

Question

Ok... this is leaving me scratching my head. I have two WPF controls--one's a user control and the other's a custom control. Let's call them UserFoo and CustomFoo. In the control template for CustomFoo, I use an instance of UserFoo which is a named part so I can get to it after the template is applied. That works fine.

Now both UserFoo and CustomFoo have a Text property defined on them (independently, i.e. not a shared DP using AddOwner. Don't ask...) that are both declared like this...

public static readonly DependencyProperty TextProperty = DependencyProperty.Register(
    "Text",
    typeof(string),
    typeof(UserFoo), // The other is CustomFoo
    new FrameworkPropertyMetadata(
        null,
        FrameworkPropertyMetadataOptions.BindsTwoWayByDefault,
        null,
        null,
        true,
        UpdateSourceTrigger.PropertyChanged
    )
);

Notice specifically that the mode is set to TwoWay and the UpdateSourceTrigger is set to PropertyChanged, again for both.

So in the style template for CustomFoo, I want to bind CustomFoo's Text property as the source to the internal UserFoo's Text property. Normally, this is easy. You just set UserFoo's text property to "{TemplateBinding Text}" but for some reason it's only going one way (i.e. UserFoo is properly set from CustomFoo, but not the reverse), even though again, both DPs are set for two-way! However, when using a relative source binding instead of a template binding, it works great! Um... wha??

// This one works
Text="{Binding Text, RelativeSource={RelativeSource AncestorType={local:CustomFoo}}, Mode=TwoWay}"

// As does this too...
Text="{Binding Text, RelativeSource={RelativeSource TemplatedParent}, Mode=TwoWay}"

// But not this one!
Text="{TemplateBinding Text}"

So what gives? What am I missing?