TFA does not actually put a stake through the heart of a fine-tuned universe.
In fact, it actually lends more support to the view that the universe is fine-tuned for one form of life: us.
The article's conclusion is based on the premise that a God would want to create lots of life, and so the constant should be more positive.
But the Biblical view is that humanity is unique (for various reasons). The value of the constant being negative would seem to support this.