Your logic may be a bit flawed. Neem, manchineel, yew, and strychnine all come naturally from a tree also. Those are all deadly in the right dose. Eating rocks is probably safer :p
It sounds like internet logic based on theory rather than evidence. Salicylic acid has an antipyretic effect on chickens.
Which would be a similar logic to a human taking a paracetamol to cope with a hot day better. I'm not sure it works that way.
I don't actually know per se, I'm not a doctor...