Multiple independent studies and reviews confirm that synaptic vesicles and their precursors are actively transported from the neuronal soma to the presynaptic terminal via axonal transport mechanisms.
The retrieved literature consistently supports the claim that synaptic vesicles and their precursors use axonal transport mechanisms (involving microtubules, actin networks, and molecular motors like kinesins and myosins) to reach the presynaptic terminal. No papers refute the claim.