"Reciprocity (altho legally that's not the correct term)"
Maybe not, but here it is in Montana LAW:
Montana Code - Section 61-3-715: BASE STATE REGISTRATION RECIPROCITY - See more at: http://codes.lp.findlaw.com/mtcode/61/3/7/61-3-715#sthash.2jSc8wsY.dpuf
Here is the actual MCA:
"61-3-715. Base state registration reciprocity. An agreement or arrangement entered into or a declaration issued under the authority of 61-3-711 through 61-3-733 may contain provisions authorizing the registration or licensing in another jurisdiction of motor vehicles, trailers, semitrailers, or pole trailers located in or operated from a base in the other jurisdiction for motor vehicles, trailers, semitrailers, or pole trailers that would be required to be registered or licensed in this state. The exemptions, benefits, and privileges extended by the agreement, arrangement, or declaration apply to motor vehicles, trailers, semitrailers, or pole trailers when properly licensed or registered in the base jurisdiction."
That is only one of many references in MCA to "reciprocity" agreements.