Not sure how to answer clearly, but here goes...
The concept of there being a need for a minimum difference in boiling points is erroneous and probably comes from rules of thumb for separating two pure phases in a single distillation using a simple apparatus.  That is, if you can boil off 100% of phase A without boiling off/condensing phase B.  Think back to WWII in Norway, when heavy water was separated from "normal" water by multiple distillation.  The boiling point difference is only 1.4 degrees, yet heavy water was successfully produced.