I feel that to make it fair. The sponsored drop should be random within a certain radius from sponsored player (e.g. 15m away from player). It could be north, south, east or west of player's location. The player should be able to trigger the drop though, within a given time frame.
With this, other players can still get a chance to loot it. Also, the sponsored player can't make it drop right beneath their feet. To make things interesting, an announcement that a sponsored drop will soon be coming down could be done. That'll keep player's spirit up.