The source of this misinformation seems to be Riseup, since I've seen other people reference it on their web site. When you surf clearnet sites, your connection comes from a Tor exit node, and there are public lists of those relays. In fact, they are added to some block lists, which many web sites use, which is why you might be blocked from accessing some sites when using Tor. Tails isn't "announcing" that you're anonymous, it's just known by the fact that your connection is coming from an exit node. You can't hide the fact that you are using Tor from the destination site unless you point the Tor Browser at a web proxy, which would stand between the exit node and the destination site. But none of that matters. You are still anonymous within the set of all Tor users, which is millions of people. The destination site knows you're browsing anonymously, but it doesn't know your identity, which is the only thing Tor claims to protect. The Tor Project is actually against obfuscating the fact that you are using Tor. They believe you have a right to surf anonymously, but site operators have a right to block whoever they want from accessing their site, and you shouldn't be hiding the fact that you are using Tor from them.