How can someone test positive for two Lyme-specific bands on western blot and NOT have been exposed to Lyme disease? What is magic about 5 bands?

Immune complexities. Lyme disease is caused by a certain type of bacteria called a 'spirochete'- they are a whole class actually of bacteria and believe it or not can be found commonly in the mouth or elsewhere in the environment. You have to reach a certain 'threshold' with Lyme testing because there could be some cross-reactivity coming from these other types of bacteria. The immune system is extraordinarily complex.
Predictive value. Tests always have to be evaluated as to their predictive value both + and - . There are findings that are falsely +, and truly +, findings that are truly -, and falsely -. A good doctor will know which are the good results that he can rely upon and the bad ones that he can discard. That is what is known as great clinical judgment. When you find someone with it, stay with him!