Glad to see you're doing your homework! 
Testing at 2-3 years means the breeder was probably doing the old urine test, which is all we had until a couple years ago. The urine test is usually done monthly starting at 3 yrs old because that is about the earliest that Fanconi starts to show up. But the urine test doesn't tell you if the dog has it or not, all it does is tell you that if the dog is affected, it will show when the actual disease is starting to manifest. But the urine glucose test won't tell you if the dog is a carrier etc. And carriers bred to more carriers can produce affected offspring. So there is still a high risk of that breeder's lines to produce fanconi somewhere. Fanconi is pretty common in Basenjis. And depending on the age of the grandparents, they could still appear free of fanconi when it just hasn't surfaced yet. The usual age of onset is 4-7, although can occur for the first time even in the teens. Now that we have a DNA marker test, even the most repsonsible breeders have found fanconi in their lines where they thought they were "clean". So it's very important to find out the DNA status of your future puppy or it's parents.
If I was in your shoes, I wouldn't get the puppy unless they did DNA testing. Losing a deposit is the least of your worries. That minimal amount is nothing compared to the thousands of dollars you'd have to spend going to vets at least twice a year and getting tests done if the dog had fanconi as well as the heartache of popping 30-40+ pills a day into their mouth, and that's if they even respond well to the treatment. (A lot of Basenjis do, but there are some that do not.) There is no cure for fanconi and it can be a very difficult disease to live with. So losing a deposit doesn't compare to getting a dog from a responsible breeder where you know to the best of the test's ability at this time that your puppy won't get sick from Fanconi later in life. At least one parent needs to test "clear/normal" for the litter to be considered "safe". Or if you test the puppy himself, he would need to test clear, carrier, or indeterminate/equivocal. All those results mean that he will not have fanconi to the best accuracy of the marker test. They are still developing a direct test which will be even more accurate, but at 90%+, the marker test is a godsend.
I would ask the breeder if they would do the DNA marker test on the parents. Let them know that you do not want a puppy unless you can better determine the status of the puppy, and you can even send them to the links where they can get the info and order the kits. If they are responsible breeders, they should have no problem doing the testing. If they won't do the testing then that might be a sign that this is not a great place to get a puppy from anyway. But if they seem nice and have done other clearances like hips and eyes, then you can still do the DNA test yourself on your individual puppy before you agree to take him home. You can do the blood sample at around 6-8 weeks old or the new cheek swab option can be done a lot earlier even it sounds like and would probably be cheaper. When they have decided which puppy will be "yours" you can order the test kit and go over and swab the puppy and send it in. It should only take a few weeks for results to come back, so you can wait to purchase your baby until you get the results.
There are lots of folks on here that can help you find a responsible breeder to get a puppy from. I know there are others in your area that would have a litter. Even if their puppies are all spoken for, I know there are other good breeders across the country that still have puppies available. It might take a bit more traveling or a plane ride to get your baby, but will be well worth it in the long run. Here is a link to the Basenji Club of America's breeder referral. This is a good place to start to help you find a responsible breeder:
http://www.basenji.org/PUBLIC/BreederDirectory.htm
Good luck and let us know how things go!
