[David] made him houses in the city of David; and he prepared a place for the ark of God, and pitched for it a tent.
It is also true that the regulation regarding "the place where God recorded his name," designated as the one and only authentic place of worship, was known throughout that whole period.  The three annual pilgrimages to Jerusalem for the great festivals of Passover, Pentecost, and Tabernacles indicate that all Israel understood this.