All who participated in the Liberation of the Philippines are eligible for the medal. The "Bronze Star" you refer to is a bronze star device (to be worn on the ribbon) NOT the Bronze Star decoration.
There were three basic criteria for award of the medal. Those who met two of three requirements are authorized to wear one star on the ribbon. Those who meet all three are entitled to wear two stars on the ribbon. Those entitled to display star device(s) are further entitled to the Philippines Presidential Unit Citation (PUC), which is yet another award (the Philippines PUC was awarded AFTER the war - and after his release from service - so it won't be listed on his separation papers).