After reading uncountable debates on the subject I've come to a few conclusions.
First the placebo effect also effects how we perceive events. A fish is sick we drop in a "medication" and the fish gets better. Would the fish have healed up in time without any changes? We will never know.
Second antibacterial means the medication kills bacteria. Cut and dry definition no ambiguity about it. "Mildly antibiotic" although commonly said does not happen. It either kills them or doesn't.
Now we have found many things that do not kill the bacteria but inhibits it's growth in some manner. Good examples of this is nutmeg and cloves. I used to run tests on these spices when I worked as a microbiologist and there we had to dilute the sample to about the 1:1000 in order to get the bacteria to grow. There usually was about 20,000 bacteria per gram of the spice but they we inhibited from growing at lower dilutions.
In a living organism if the bacteria are inhibited from growing the immune system can catch up and destroy them. So just slowing them down enough is sometimes as effective as antibiotics (if the immune system is somewhat healthy).
Third as this is a living system there are literally thousands of variables in the host/pathogen relationship that can determine who wins. Antibiotics have a very high success rate because they actively target and destroy the pathogen. Other treatments may work but it's a larger gamble with your fish's life.
BTW for your infected shin
SubRosa, my stomach almost turned over at the site of that one. Nasty. Honey is has bacterial inhibiting characteristics (by making the pathogen literally dry out) and the tea tree oil also has been shown to be antibiotic by this mechanism. "... disrupt the permeability barrier of cell membrane structures and the accompanying loss of chemiosmotic control is the most likely source of its lethal action at minimum inhibitory levels."
But please leave the nasty pictures off . Some of us like to eat while perusing this site.
Cox, S.D. et al., 2000. The mode of antimicrobial action of the essential oil of <i>Melaleuca alternifolia</i> (tea tree oil).
Journal of Applied Microbiology, 88(1), 170-175.