How to associate iPhone application with _every_ file type?

There is iPhone app "Another Mail Client" that should be able to open any file to send it as attachment. So, I want to associate this application with any file with any extension.

Following the documentation, we should declare support for files with the root UTI-type public.data – any file should belong to this type. It works, but not at all. In this case, our app will not be able to open any file, but only those which have already been registered in the system. For example, if in any application (e.g., dropbox) we'll try to "open in..." file with an unknown extension (file.unknowntype) using UIDocumentInteractionController, then the answer will be negative despite the fact that we have already registered our application and it supports the root UTI-type public.data. But, if you install another application, which supports files with extension (*.unknowntype), then our application will also be able to open these files and will appear in "open in..." application list.

UPD: @Gabriel This is CFBundleDocumentTypes part of my info.plist file:

<key>CFBundleDocumentTypes</key>
<array>
    <dict>
        <key>CFBundleTypeName</key>
        <string>MyMail</string>
        <key>LSItemContentTypes</key>
        <array>
            <string>public.data</string>
        </array>
        <key>CFBundleTypeRole</key>
        <string>Viewer</string>
        <key>LSHandlerRank</key>
        <string>Default</string>
        <key>CFBundleTypeIconFiles</key>
        <array>
            <string>Icon29.png</string>
            ...
            <string>Icon114.png</string>
        </array>
    </dict>
</array>