Usenet services are more concerned about removing illegal content when it's reported than what users are downloading. You can get a provider that doesn't log download activity and accepts Bitcoin payments, you'd want to use its SSL connection, and you can go through a VPN as well (some Usenet providers even bundle VPN services with their Usenet subscription). It's generally much safer than torrenting from a privacy standpoint where anyone on your tracker sees your IP (or, once again, your VPN's IP). I'm not aware of any Usenet server that says it didn't log downloads secretly doing so because it's really not in their interest to lie about it. They know why people are subscribing.