Final answer:
The discharge from a single excitatory presynaptic terminal usually isn't enough to cause an action potential in the postsynaptic neuron as multiple EPSPs are often needed to reach the action potential threshold.
Step-by-step explanation:
The statement that the discharge of a single excitatory presynaptic terminal almost never causes an action potential (AP) in postsynaptic neurons is true. In the context of synaptic transmission, the release of neurotransmitter by the presynaptic neuron leads to an excitatory postsynaptic potential (EPSP), which is a depolarization that makes the postsynaptic neuron more likely to fire an action potential. However, typically a single EPSP is insufficient to reach the threshold required to generate an action potential in the postsynaptic neuron, and summation of multiple EPSPs, often from different presynaptic neurons, is necessary for the postsynaptic neuron to reach the action potential threshold. This mechanism serves as a filter to ensure that only significant and coordinated inputs lead to post-synaptic neuron excitation.
EPSPs around the same time for the postsynaptic neuron to be depolarized enough to fire an AP. This process is called summation and occurs at the axon hillock. Additionally, synaptic inputs from many presynaptic neurons, some excitatory and some inhibitory, can cancel out EPSPs and vice versa. The net change in postsynaptic membrane voltage determines whether the postsynaptic cell reaches its threshold of excitation needed to fire an AP.