Seeing someone improve after taking antibiotics is not indicative of them having an infection that’s being treated by the antibiotics.
It could be. It is also not indicative of them not having an infection. It just depends.
As per my limited understanding, anti-inflammatory antibiotics are more relevant for respiratory and auto-immune conditions, not too broadly otherwise. If the source of the inflammation is not treated, the temporary reduction in inflammation is pointless because the inflammation will return.
If someone is suffering as badly as the people in the article and the doctors have no idea what is going on, then the benefit of taking antibiotics outweighs the risks.
You seem to forget that this patient is suffering. Having their gut biome wiped out is nothing compared to them chronically suffering as they are.
For example, in a specific case, for acute intestinal pain, amoxicilin with clav was being advised, but the etiology+location+correlations suggested that mere metronidazole alone would suffice, and it did. It's case by case.
If you are truly convinced it's a bacterial infection, then you can use a broad spectrum antibiotic, e.g. amox+clav, which you can get on your own, but I would simultaneously take a probiotic twice daily to prevent the gut from getting colonized by bad microbiota, e.g. C diff. Even so, sometimes a different antibiotic is needed, e.g. doxycycline.
During the early months of Covid I had to take chloroquine. The point again is that no one medicine really is broad enough.