True. Medinah was originally a Jewish settlement named Yathrib some of whose elders believed that Muhammad might be the the Messiah. They welcomed him and his followers into their settlement. Muhammad used it as a base for raiding caravans for many years.
Indeed the very name Medinah is Jewish. In Hebrew that word means "market-place" thus a place where law and order and standards and courts would prevail, and one could safely trade.
Thus "medinah" can mean "city-state" or today even "state" in the sense of an area under a common government and laws, thus an Israeli passport says on the cover Medinat Yishrael.
In turn, of course this is from "dina," meaning law or code of law, with the particle "m" which can mean "of" or "subject to."