It happened when my husband deployed, because I moved to my hometown. My hometown BAH rate was lower then Denver BAH rate.
There is a "loophole" that the military can use (the Navy does it all the time) about the BAH. It's based on the service member's duty station -- unless the family can't go there (like unaccompanied orders) -- OR - unless they decide "for the best interest if the service" to provide it where the family is. (Basically, they realize you aren't there, like you went home for the deployment, and the BAH where you went is lower and they want to be cheap... I've seen this happen - not always, but it can.)