"To find two identical spirals among two cultures of which one was the older and was known to have influenced the other (and perhaps vice versa) is enough to raise questions concerning the origin of the spiral.
And the math that it required."
Maybe they just saw a snail and admired the spiral shape of the shell. No math needed, but it is a perfect expression of the golden mean.
Without taking a stand on the accuracy of the claim, the article states that the Archimedes spiral is not found in nature, and it specifically mentions that snail shells do not follow that pattern.