Whether it's a coincidence or not, what difference does it make?
I think it makes a lot of difference in our world view. If it's not designed and we are just globs of chemicals making random chemical reactions, then that affects all kinds of things, not the least of which is how can we even trust logic, if it also is a product of happenstance. But if logic is designed like the universe, then we have a basis of how we can know anything.
Barrow & Tipler, in their standard treatment, The Anthropic Cosmological Principle, admit that "there exist a number of unlikely coincidences between numbers of enormous magnitude that are, superficially, completely independent; moreover, these coincidences appear essential to the existence of carbon-based observers in the Universe."
- there is the same number of electrons as protons to a standard deviation of one in ten to the thirty-seventh power, that is, 1 in 10,000,000,000,000,000,000,000,000,000,000,000,000 (37 zeros)
- the 1-to-1 electron to proton ratio throughout the universe yields our electrically neutral universe. In other words, the electron and the massively greater proton have exactly equivalent opposite charges
Reasoning that the universe isn't designed because its here and wouldn't self exist if it was different is about as satisfying as a doctor saying that the reason your child is sick is because he's not doing well.
That kind of thinking is well outside of popular atheist thinkers:
Stephen Hawking: "The remarkable fact is that the values of these numbers seem to have been very finely adjusted..."
British astrophysicist Paul Davies wrote, "There is now broad agreement among physicists and cosmologists that the universe is in several respects 'fine-tuned' for life. ...carbon, and the properties of objects such as stable long-lived stars, depend rather sensitively on the values of certain physical parameters... it is fine-tuned for the essential building blocks and environments that life requires."