No, it's never promised unlimited — it's always had usage limits: 20× the usage of their regular Pro plan, with a limit of 50 sessions per month (a session being a 5-hour window), although I don't know if they ever enforced this.

They appear to have removed reference to this 50-session cap in their usage documents. (https://gist.github.com/eonist/5ac2fd483cf91a6e6e5ef33cfbd1e...)

So even if these mystery people Anthropic reference who did run it "in the background, 24/7", they still would've had to stay within usage limits.