Final answer:
The assertion that a neuron will fire an action potential solely with excitatory input is misleading; the neuron will only fire if the cumulative excitatory inputs are strong enough to surpass any inhibitory inputs and reach the threshold needed for an action potential.
Step-by-step explanation:
The statement that if a neuron receives an excitatory input from another neuron, it will fire an action potential is not entirely true. A neuron can receive both excitatory and inhibitory inputs from multiple neurons. These are known as Excitatory Postsynaptic Potentials (EPSPs) and Inhibitory Postsynaptic Potentials (IPSPs), respectively. EPSPs result in local membrane depolarization, whereas IPSPs result in hyperpolarization. For an action potential to occur, the net effect of the summed EPSPs must be strong enough to overcome any IPSPs and reach the threshold of excitation at the axon hillock.
Thus, it is the overall summation of these inputs that determines if the neuron will fire. If the threshold is not reached, no action potential will occur. Therefore, the neuron will only fire an action potential if the excitatory inputs sufficiently outweigh the inhibitory ones and bring the membrane potential to a critical level often around -60mV.