I've looked into this a bit more.
I think it's almost certainly down to trust level. Look at this MS article: http://msdn2.microsoft.com/en-us/library/ms998326.aspx
I suspect that 1&1 have medium trust level within their shared environments (fair enough really). I'm using shared hosting and presume you are as well?
However, looking at the dnn web.config file, it does mention about compatibility with medium level trust, so may be the resolution of this may be possible on the dnn side. I somehow doubt if 1&1 will want to reduce their trust level for us, if dnn really requires it!:
<sectionGroup name="dotnetnuke">
<!-- the requirePermission attribute will cause a syntax warning - please ignore - it is required for Medium Trust support-->
<section name="data" requirePermission="false" type="DotNetNuke.Framework.Providers.ProviderConfigurationHandler, DotNetNuke"/>
<section name="logging" requirePermission="false" type="DotNetNuke.Framework.Providers.ProviderConfigurationHandler, DotNetNuke"/>
<section name="scheduling" requirePermission="false" type="DotNetNuke.Framework.Providers.ProviderConfigurationHandler, DotNetNuke"/>
<section name="htmlEditor" requirePermission="false" type="DotNetNuke.Framework.Providers.ProviderConfigurationHandler, DotNetNuke"/>
<section name="navigationControl" requirePermission="false" type="DotNetNuke.Framework.Providers.ProviderConfigurationHandler, DotNetNuke"/>
<section name="searchIndex" requirePermission="false" type="DotNetNuke.Framework.Providers.ProviderConfigurationHandler, DotNetNuke"/>
<section name="searchDataStore" requirePermission="false" type="DotNetNuke.Framework.Providers.ProviderConfigurationHandler, DotNetNuke"/>
<section name="friendlyUrl" requirePermission="false" type="DotNetNuke.Framework.Providers.ProviderConfigurationHandler, DotNetNuke"/>
<section name="caching" requirePermission="false" type="DotNetNuke.Framework.Providers.ProviderConfigurationHandler, DotNetNuke"/>
<section name="authentication" requirePermission="false" type="DotNetNuke.Framework.Providers.ProviderConfigurationHandler, DotNetNuke" />
<section name="members" requirePermission="false" type="DotNetNuke.Framework.Providers.ProviderConfigurationHandler, DotNetNuke" />
<section name="roles" requirePermission="false" type="DotNetNuke.Framework.Providers.ProviderConfigurationHandler, DotNetNuke" />
<section name="profiles" requirePermission="false" type="DotNetNuke.Framework.Providers.ProviderConfigurationHandler, DotNetNuke" />
</sectionGroup>