That's the kind of situation that watermarking handles well. With no time to remove the watermark, it would be straightforward for the stream source to find the offending stream consumer and shut down their stream.
And we're both assuming that the people running those mirrors won't work out a way to disable the watermarks in real time. I've not read up on digital watermarking technology, but it's hard to imagine that it's bulletproof.
And yes, I'm assuming that robust-enough watermarking methodology is possible. I don't think it has to be bulletproof, I just think it has to be good enough to enable cancelling enough stream consumer accounts to deter casual mirror-ers. DRM isn't bulletproof either; watermarking is preferable for users because it doesn't require that the stream producer take control over your machine.