No you don't. As the parent poster says, if you screw up, you want to be able to figure out why. Unless you enjoy digging for months for biases in large incomplete datasets with a panicked guy screaming at you, you'll have at least a couple dozen output neurons (you can always also have a yes/no one if you like).
In practice all the parameters will fire to some extent, right. You need some function to resolve it. Generally people start out by giving the "no's" preference, then you switch to something more complex, then some product manager suddenly declares the law: give "yes" preference.
So the output of that network will be a) 15.15% b) 74.3% c) 55% d) ... and so on. The highest values are considered and some function chooses from that.
It's how it works in the human brain as well, but the solution that wins is the one that gets control of the brainstem. Generally being the first to respond is pretty much guaranteed to get you control, but something else may override you later. The human mind, in reality, is not a single whole, but is ~300 separate minds that could, if it were necessary, operate alone. Each of those is constantly coming up with responses to inputs, and they're all linked through the brainstem, which is also the link to the rest of the body (except the eyes, which are only input to ~6 of them, and the ears, which also are connected directly to ~6 of them. That seems to be to enable brain-eyes bandwidth to be ~100000 times more than all the bandwidth it has to the body, and brain-ear bandwidth ~100 more).