I think what they're saying here is that you're not just suppressing a symptom, you're suppressing a sickness fighting mechanism.
He said that.
Fever isn't just a symptom. It's a defense mechanism. The idea is that use of antipyretic drugs may make the infection worse.
The sentence is constructed, weirdly, but it's meant to say that fever is "killing off unknown foreign bodies"
Pain being a way to let you know that something is damaged is close to true--close enough not to quibble with. But fever is not a way to let you know that foreign bodies are being killed off--that's his claim, and it's wrong.