NBA spokesman Tim Frank explained the decision in the league's statement (h/t ABS-CBN News):
"The NBA's agreement with FIBA stipulates that NBA players can participate in the Olympics, the FIBA Basketball World Cup, Continental Cup competitions, and associated qualifying tournaments. Because the Asian Games are not one of those competitions, NBA players are unable to participate. In accordance with the NBA's agreement with FIBA, Jordan is welcome to represent the Philippines in the agreed-upon competitions."
The Philippines national team head coach Yeng Guiao had already included Clarkson on the 12-man roster, according to Charmie Lising of ESPN.com, with the hope that the NBA would grant Clarkson permission to participate in the tournament.
Per that report:
"SBP officials were still working late Friday on obtaining the necessary permits that would have allowed Clarkson to represent the Philippines in Indonesia. According to Guiao, who had not received word from the NBA or the Asiad organizers when speaking to ESPN5 late Friday, they were also looking to fly Clarkson to Manila before the team heads to Jakarta on August 12."
Having Clarkson for the tournament, who is Filipino American, would have been big for the Philippines. The 26-year-old averaged 13.9 points, 2.7 assists and 2.7 rebounds per game in stints with the Los Angeles Lakers and Cavaliers this past season.
As it stands, the Philippines will likely try to add Don Trollano to replace him.
"If the organizers will allow it, we'll add [Trollano] so we'll have 12 players," Guiao said over the weekend. "If not, it's OK that we only have 11."