Not a good example at all. People of Swat are Pakistanis, they dont need anyones permission or visas to goto Karachi. Will the state of Washington deny entry to a person from Michigan? 
No.
Furthermore, at a time of war and calamity, even countries open up their borders. Also, denying a visa based on the basis of ethnicity is discrimination.
Nope, any Pakistani should be able to go and reside in any city of their choice. Just recently a Pakhtun named Imran Khan was not allowed to enter Karachi and section 144 was imposed. It happened many times before. Of course, with the independent judiciary in place, he threatened to go to the SC and they had no choice but to pull back the silly restriction.