I think the problem is somewhere else in the control tree. Can you post more details?
Here is a sample xaml code that works as expected:
<Page xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation" xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml">
<Grid>
<Grid.Resources>
<XmlDataProvider x:Key="flickrdata" Source="http://api.flickr.com/services/feeds/photos_public.gne?tags=flower&amp;lang=en-us&amp;format=rss_200">
<XmlDataProvider.XmlNamespaceManager>
<XmlNamespaceMappingCollection>
<XmlNamespaceMapping Prefix="media" Uri="http://search.yahoo.com/mrss/"/>
</XmlNamespaceMappingCollection>
</XmlDataProvider.XmlNamespaceManager>
</XmlDataProvider>
<DataTemplate x:Key="itemTemplate">
<RadioButton GroupName="One">
<Image Width="75" Height="75" Source="{Binding Mode=OneWay, XPath=media:thumbnail/@url}"/>
</RadioButton>
</DataTemplate>
<ControlTemplate x:Key="controlTemplate" TargetType="{x:Type ItemsControl}">
<WrapPanel IsItemsHost="True" Orientation="Horizontal"/>
</ControlTemplate>
</Grid.Resources>
<ItemsControl
Width="375"
ItemsSource="{Binding Mode=Default, Source={StaticResource flickrdata}, XPath=/rss/channel/item}"
ItemTemplate="{StaticResource itemTemplate}"
Template="{StaticResource controlTemplate}">
</ItemsControl>
</Grid>
</Page>
P.S.: In order grouping to work elements radio buttons should have same parent (as they usually have when generated from ItemsControl)