@saving NO ! Don't call it inbreeding - because in this case it isn't. Our dogs are all closely related but the pairings were out-crosses.
Basenjis, IMNSHO, should be line-bred. Everything Marvin and I produced in about 40 years of breeding, was line-bred on Donner. Ch and Irish Ch Domewood Donner. We line-bred quite closely, crossed right out and then came back in again to fix type.
Think about it in the wild. A pack of Basenjis is not owned by a person but by a village. The pack runs wild and the Alpha male mates with his aunts, his neices, his grand-daughters, his sisters, his mother and just about any female in the pack. Close line breeding. And Basenjis as a Breed are one of the oldest - one of the 6 original canines. They have survived in recognisable construction for - so people say - 6000 years.
Look back through some of the oldest pedigrees and you will see this continuing -