It's not assuming zero probability. It's assuming independence. Under the original model, it's possible for all the women to get positives, but only 1% to actually have breast cancer. It's just that a better prior would give a much higher probability.
Is there any practical difference between "assuming independent results" and "assuming zero probability for all models which do not generate independent results"? If not then I think we've just been exposed to people using different terminology.
Here's the new thread for posting quotes, with the usual rules: