Liz Buchanan BVSc MRCVS
Hi Ian I'm sure that if your vet has done tests and says that they have found there to be bacteria in those lesions, they will be right; indeed, the skin looks to have lost its superficial protective barrier and appears quite raw, leaving it vulnerable. These days we treat bacterially-infected skin with antibiotic shampoo rather than antibiotic tablets. If the infection is only superficial, this spared medication affecting the balance of bacteria in the gut, for example.
Often, such lesions also contain yeast infection requiring an anti-yeast shampoo also; perhaps the antibacterial shampoo also contains agents that address yeast or other superficial opportunists.
However, another question is why bacteria +/- yeast would have invaded the skin in the first place. My skin comes up against all sorts of bacterial pathogens every day (I used to put my hand up cows' bottoms as part of my job), yet I have seldom needed treatment for a skin infection. Healthy skin, whether it was designed or evolved for the purpose, keeps bacteria out.
Therefore in this case, it is likely that something may have weakened the skin or caused inflammation and the cause of that inflammation may need to be addressed. I wonder about things like allergies, lymphoma, autoimmune conditions, mites and so on.
I wonder what country you are in and whether there are parasites that you need to be aware of.
Obviously I know very little about your dogs' specific case, so your vet's opinion will likely be more helpful than mine. If they have run out of options from here, they might be able to refer you to a dermatologist for more information.
Best of luck.