I feel like the more you learn about neuroscience, the more you learn how precise and complex neural information processing is. For instance, there's evidence that at least some neurons "record" information about their activity in the form of RNA. Also the placement of synapses in the dendritic arbour matters, and some synapses can act like logic gates with respect to the synapses farther down the same branches.

I think there almost certainly must be neural behavior which codes fairly simply based on rate, but it's very difficult to believe that there isn't neural computation based on precise timing relationships.