Definition of synaptic strength
Synaptic strength is defined as the average amplitude of postsynaptic potential evoked following a presynaptic action potential.

This is a correct definition. Synaptic strength is a fairly abstracted measure. It can be influenced by both presynaptic (for example: number of vesicles/concentration of neurotransmitter per vesicle) and postsynaptic effects (for example: receptor number and composition). So yes, changes presynaptically such as the character of an action potential can influence synaptic strength, but that isn't a problem: we still represent this as part of the synaptic strength if it affects the average postsynaptic potential.
Biologically, action potential amplitude in the axon does not really matter much for synaptic release, but local conditions in the presynaptic terminal that influence calcium influx do. The section on presynaptic inhibition in the answer here may help a bit.