I told him that he was wrong.

him为间接宾语，that从句为直接宾语从句。当这个句子改为被动句，间接宾语作了主语，that从句保持不变，改称为保留宾语：

He was told that he was wrong.

所以to be told that he was wrong 就是一个带有保留宾语的被动不定式。

不定式作宾语，与句子主语有逻辑主谓关系。当主语与不定式为被动关系时，不定式要用被动语态，所以：

He didn't like to be told (that) he was wrong.

这个分析和你的句子结构完全相同。