1.先纠正一个语法理解错误,I am not against students taking phones?与 This story is about a man saving a child's life.后面的动词+ing 是现在分词,不是动名词.students taking phones 与 a man saving a child's life 是逻辑主谓结构.taking phone 是 students 的动作；saving life 是 a man 的动作.
2.另外除了动名词外可以加过去分词吗?回答：可以的.就拿你的例句做一小小的改动：This story is about a child's life saved by a man.
前面 meisuo87 的理解是对的.