>> “Bullet begins to drop as soon as it leaves the muzzle.” <<
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Not if it is aimed upward on a ballistic trajectory.
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The statement “...begins to drop as soon as it leaves the muzzle.” is correct. The drop manifests as a reduction in the vertical component of the projectile velocity over time.
If one dropped an object from near the surface of earth, it would accelerate at a nearly constant rate, in the downward direction (toward center of mass of the planet.) Similarly, the projectile in this example does the same thing, as described above. Effects of aerodynamics, and relativistic effects, and the location of the center of mass of the universe, and possibly others, have been dismissed from this discussion.
You missed the whole point.
The skeptics were misdiagnosing the question, not realizing that the shooter had simply determined the needed elevation of the launch trajectory by trial and error over time, which worked only for the particular situation he had analysed.
New target, start over, so big deal, his chance of hitting the new target is zilch.