Incidentally, it's also the same story for colorectal cancer, the 2nd most common type of cancer. Here's another study on the topic. [1] They have a survival rate of 88.6 vs 85.9 for breast cancer, but it's a large observational study that's not normalized, so the confounders/biases there probably explain the reduction in survival rate at non-NIC hospitals. Colorectal cancer is even smaller - 0.2%.
NIC hospitals only showed a significant effect on cancers with low survival rates, and especially on rarer cancers. For instance with pancreatic cancer 93.8% of people who went to a non-NIC hospital were dead in 5 years, by contrast 'only' 87.5% of NIC hospital patients were. Feel free to look up the data yourself. I'm not searching for cherry picked studies, there are none - as there seem to be oddly few studies on this question, and they all say the same thing. What benefit there is is quite small, and heavily driven by extremely rare things.