No. Sound travels at a known velocity of about 1100fps. Therefore, if one can measure the time between the shot leaving the gun, and hitting its target, one can come to a reasonable assumption. Of course, you have to figure in flight time of the bullet because the bullet will be in the air and slowing down with the sound wave close on its heels. For a 3/4 mile shot with an initial velocity of 1600fps, I would assume that the bullet and sound wave would arrive nearly simultaneously. The sound wave would overtake the bullet in flight. Measuring this by ear is impossible. Sure, maybe within plus or minus one mile you could guess then you'd surely be right!
This presumes several things. First, you have to know the initial velocity of the bullet as well as it's time of flight. For that, you'll need to know the Ballistic Coeficient of the bullet. Also, you must know that the sound you are hearing is indeed the shot and not an echo or sonic boom. I'd assume that the reporting party did not know the velocity or BC of the bullet but might have known the lightning trick.
With Lightning, you can measure distance because the first cue is visual. You SEE the bolt and can therefore begin to count. When you hear the thunder, just multiply the number of seconds by 1100 feet and you're there. The same does NOT apply to bullets, but can apply to muzzle flash!
Bottom line, he was wrong.