BS has nothing to do with them not 'following proper sterile procedures'. It is just common to happen after treatments as the OP described, however, in the west we never give out such medicine upfront, only once it became a problem.
Here they do give them out upfront, one because they cost nearly nothing and 2, because people rather take cheap pills than having to come back with a tennis ball mouth caused by infection, to then need a paid procedure and still take the antibiotics.
But yes, for many of the people they do heal naturally without any of that. The fact they hand it out does not mean you should take it as if it is candy, just to save you money and not make you need to come back, as a prep.
If something is not logical, look at the money costs and trails, there is your answer.