Domestically, he has played for Khan Research Laboratories, Lahore, Lahore Eagles, Lahore Lions, Lahore Qalandars, Pakistan A and Huntly (Scotland) during his career. He was the captain of Lahore Qalandars in the first edition of the Pakistan Super League.
Not all players in Pakistan remain on the same team for their entire careers.
This player has played for multiple teams in Pakistan, including multiple teams in Lahore.  So the statement is correct and not all players in Pakistan play their entire careers on the same team.  The system problem didn't get it right because they don't recognize that each team from Lahore is obviously from Pakistan, since they're in the same city and we know that the Lahore Qalandars are in the Pakistan Super League.