It should be noted when a provider and a client agree on such arrangements they are doing it by choice and therefore are assuming the risks, knowingly or unknowingly. Those of us who don't partake in the such activities simply need to protect ourselves by using protection, which is also an alternative choice.
Amoxicillin is an antibiotic. According to WHO, there are three bacterial (chlamydia, gonorrhoea and syphilis) and one parasitic STIs (trichomoniasis) that are generally curable with existing single-dose regimens of antibiotics. So Amoxicillin does actually work to a certain extent, however it is not the normal antibiotic of choice for treatment of the noted STIs. Amoxicillin is normally used in treatment of dental abbesses as well as chest and sinus infections. This might explain how such characters have the drug readily available.
However there are three other STIs that are viral. These are herpes, HIV, and hepatitis B. There are no cure for these, The most effective medications available are antivirals that can treat the disease by reducing it's severity, but they cannot cure the disease.
Taking these factors in to account it appears that the aforementioned characters could be misleading vulnerable ladies, likely on LL, she could be independent or associated with an agency. The best thing those of us who don't partake in the sexual activity is to use protection (condom) and if we have a good and close client/provider relationship talk to our favorite ladies, awareness and education is the key.
Regardless of if you are a provider or a client, I encourage you to have a read and read more if you wish:
Sexually transmitted infections (STIs).