The Fibonacci sequence is merely an artifact of the way nature works. So, it appears naturally, pretty much like other mathematical descriptions of nature like the Feigenbaum number. It's not a magical thing "designed" into nature; it's a consequence of a few simple rules (or maybe just one) by which it all works.
So the arrangement of leaves on a stem, that maximizes exposure to sunlight follows the Fibonacci sequence. Not because some space alien designer invented it but, like evolution, because the Creator made those rules at the beginning. No magic, just creation.