Nothing necessarily wrong with doing a treatment based on slight, educated guesses. Wick has been treated successfully for ringworm, URIs, and a tooth infection, all without doing tests. Generally antibiotics when prescribed at a realistic dose won’t really harm a healthy rabbit. Potentially an upset stomach, but if it’s precautionary, it won’t kill it unless it’s a very sensitive rabbit.
Did your vet attempt to look at the back molars with an otoscope? This can give a somewhat better idea of teeth problems which can cause excessivice salivation, which leads to crust and fur loss.
How was the test for ringworm conducted? That honestly looks exactly like Wick when he had ringworm. Ringworm isn’t a single bacteria type. There are multiple bacteria which can cause ringworm. Ringworm is actually just a visual descriptor, rather than the infection. Ringworm is a descriptor for fungal infections. Generally Wick’s vet doesn’t do any tests for things like this because there’s always a chance the test is contaminated or wrong, so sometimes it’s good just to start treating to see if it helps instead of letting it get worse.
Is that black patch new fur coming in? I’m unsure what necrotic skin looks like from experience, but I know that turns up as black as well. If it seems like new fur growth, that’s actually supporting evidence for ringworm, because ringworm spreads continuously and will abandon some past area as it spreads since it cannot live there (hence the name ring worm. Fur loss in a circle and as it moves out, fur regrows inside where it used to be, making a worm of bare skin).
The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.