I think this question is based on a misunderstanding of the dictionary definition.
(of people) to say the opposite of what someone else has said, or (of one fact or statement) to be so different from another fact or statement that one of them must be wrong
The words "of people" and "of one fact or statement" appear in parenthesis to mark that there are two parts to this definition - one that can be said of people, the other that can be said of facts or statements. In other words, you can contradict a person or you can contradict a fact.
- I contradicted him. <--(of people)
- That contradicts his statement. <-- (of one fact or statement)
It doesn't mean that you can insert the words "of people" into the examples. The sentence you quoted as an example is complete.