The only way to rule out infection in the urine is to run a culture. Just because the CBC was normal, does not mean there isn't infection in the urine. In fact, in most cases of urinary tract infections, the CBC is normal. However, in cases of kidney infections, one would expect the WBC count to be elevated. I wouldn't simply rule an infection out just based on a CBC though. That is very presumptuous. If a urine culture has not been done, I don't see any harm in doing it.
There are numerous "toxins" that can cause kidney damage. Of course, antifreeze is the most common, and there is a test for that. If they ingest it, it is usually fatal, so I guess I wouldn't be leaning towards that. Unless you have an idea of what type of toxin your dog may have had contact with, it is very unlikely to be able to just run a "screening test" that checks for all the possible toxins that cause kidney damage. Dogs get into things that we are not aware of all the time. The best thing to do is look through your house at the chemicals you have that he might have had exposure to. Your vet may be able to help you research if any can cause kidney damage. A vet list I am on lists Lysol as one of the chemicals that can cause renal tubular damage. Lead poisoning, mercury poisoning can also cause this damage, but it is more rare in dogs to see this unless you have lead paint in your house. There are plants that cause kidney damage also, the most common one being lillies. I have seen many cats get ill and even die from ingesting a lily plant leaves, but I haven't met any dogs that have eaten lillies, but it is a possibility. Certain antibiotics and other drugs can damage the kidneys, and something he was on when he had parvo may have affected the kidneys. And yes, someone may have tried to poison him. But again, unless we know what we are looking for, there won't be a specific test to run, we simply find out when problems arise that damage has been done by the toxin. Most cases, the damage is permanent if the damage is done to the kidneys.
Fanconi's syndrome is most common in Basenji's, but it does occur in other breeds, but rarely. It is genetic in Basenji's. What I've described above--all the causes of renal tubular damage--could be described as "acquired" Fanconi's syndrome, and this can occur in any breed of dog.
You will need the help of an internist to diagnose this condition. There are several things that are recommended to be done, including urine cultures, kidney ultrasounds, measuring for electrolyte abnormalities in blood and urine. This site lists what is done for Basenji's: http://basenjicompanions.org/health/fanconi/suspect.html , and these tests will probably need to be done in your dog to diagnose tubular damage also. I understand you do not like the specialist near you. Is there anyone else you can go to? It just sounds like your vet isn't able to continue with the diagnostic tests, and unless a specialist gets involved, you might never know for sure what the diagnosis is. As a general practitioner myself, I would definately have to refer a case like this, it is just so rare a problem, and complicated to diagnose.
There are special diets and supplements that are recommended, but the symptoms like excessive urinations do persist, I believe.