There’s debate over how much timing actually matters vs the rate of firing. Some people do believe in precise spike timing but I would say the general consensus is that spiking rate is a better measure of the current state of a system. There’s significant noise (as far as we can tell) in a neuron’s timing and it’s best modeled with a poisson process so we tend to think of it as rate coding which we can at least hand wave as viewing an RNN with a ReLU approximating.

Generally you can take a geometric view of this where certain features in a stimulus covary with neural activations in the same way they will with RNN “activations” which is at the real core of why people model things this way. The general idea being a dot product in an RNN can tell you something about what features are relevant for a task and we can look for hints of the same information being encoded in neural data. Certainly not everyone is in agreement on this though.