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The idiom is literally “fight fire with fire”

Also, “the enemy of my enemy, is my friend”

Maxim 29. The enemy of my enemy is my enemy's enemy. No more. No less.

That doesn't mean what they're doing isn't to your advantage.

> “the enemy of my enemy, is my friend”

That one basically never leads to anything good.

Well, none of these are “words to live by” so you’re not wrong.