It’s a good argument. But in reality, any argument against fine-tuning will be accepted, whether it makes sense or not. It is only the defenders of a rational universe who need to make sense. And that’s not for the other guy; it’s for you.
Here’s Scientific American in a more entertaining mode. Remember when Deep Thought, the computer in Hitchhiker’s Guide to the Galaxy (1979) spit out the Answer to the great question of life? It was: 42 But 42 does have some interesting features.