You can't really put a useful p-value on that.
To calculate a p-value (roughly spoken), you need to start with a single hypothesis. Then you gather data and the p-value gives you the probability that your data occurs while your hypothesis is false. When you start with a finite set of multiple hypotheses, you need to take that in to account when calculating your p-value.
When you start with data and come up with a hypothesis afterwards, you would have to find the whole potential space of all hypotheses. So, for example, how many hospitals are there? Do you only consider US? Do you only consider nurses or other employees as well? What about only four nurses would that have made it to the news? What about other forms of cancer? What about time? Do you consider the time period of the last 50 years? As you think about what might have made the news, the set of hypotheses grows bigger and bigger and as it approaches infinity, the p-value for any data would approach one. Because when you have a very large set of unlikely hypotheses, the probability that your data accidentally supports one of them is quite large.
That's what parent was talking about.