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There is a huge difference in dose between “bacteria in your mouth producing an antibiotic” and “taking an antibiotic for an infection”. Bacteria, even the normal bacteria currently present in your mouth even without taking BCS3L-1, constantly produce antibiotics to kill competing bacteria. But they only produce tiny amounts, enough to affect the competitors in their immediate vicinity, but not nearly enough to cause any kind of systemic effect. If they did, you would already be experiencing these effects right now from all the other antibiotics produced by other bacteria in your mouth. In contrast, antibiotics for medical use are usually given in doses measured in the hundreds of milligrams or even grams, far more than mouth bacteria could ever possibly produce.