As it says on wikipedia
It was known as the Yugoslavia national basketball team until April 1992 and the FR Yugoslavia / Serbia and Montenegro national basketball team until June 2006. When Serbia became independent, it became the successor state to the Serbia and Montenegro and, therefore, the results of previous state FR Yugoslavia / Serbia and Montenegro rightfully belong to it.
Yugoslavia was destroyed in 1992. so after 1992. it wasnt "that" Yugoslavia anymore(With Croatia,Slovenia,Bosnia and Macedonia) it was only Serbia and Montenegro but Serbia and Montenegro arent successor of "that" Yugoslavia the one before 1992. so these results do not belong to Serbia,all players who has played and won these medals were actually and mostly Serbs,actually Serbia have won 2x WC and 1x silver on olympic games and 3x Eurobasket