Associating Visibility with a DataContext

I have a value converter that converts null to Visibility.Collapsed. Now I'm trying to use it in a user control so that the whole control is reset when the DateContext is null

The control is as follows:

<UserControl x:Class="PhoneApp.Controls.Header"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
    xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
    mc:Ignorable="d"
    Visibility="{Binding Converter={StaticResource ToVisibility}}"
    d:DesignHeight="150" d:DesignWidth="480"> <-- some body here -->

And it is used as

<my:Header DataContext="{Binding SectionHeader}"/>

Where SectionHeader is a property of the view model.

I have a similar control where I do not bind a DataContext, but some kind of custom DP and collapse there works fine. However, in this case, the value converter seems to be called only when SectionHeader! = Null. When it is zero, the control is displayed with empty children.

I thought that DataContext is not used here, but control with it is much cleaner.

DataContext ? ?