Do people think you can do a bit of maths and magically there's no serial killer?
If it's shown that statistical arguments for there being a serial killer were flawed, then there's no safely convicted serial killer.
You don't need maths you need common sense.
Common sense works for common things. It's less good at judging the chance of one-in-a-million events. That's why so many people buy lottery tickets.
Common sense would say it's unlikely that two people in a group of 21 random strangers share a birthday; but surprisingly, it's more likely than not. Common sense would say, that if a 99% accurate test says someone has a disease, then there's a 99% chance they have it; but in fact, if only .01% of the population has the disease, then the chance is only 1%. Common sense would say that, in the Monty Hall Problem, there's no point in switching your choice (and we argued all night about it when it was given in a college probability course); but actually, switching doubles your chances of winning. Common sense would say that, to know if a drug works, you should just ask people who took it; but need double-blinded randomized placebo-controlled studies to really know.
At least you agree her numbers were higher than all the other nurses
We don't have "all the other nurses'" numbers gathered the same way as hers, so no, I don't agree. You have to compare like with like. "Her numbers" simply aren't the same kind of "numbers" as other nurses', unless all numbers were gathered blindly the same way for all and then compared for different staff.