This is not mathematics though, nor science, it's just the meta-mathematical philosophical opinion of a guy (mostly self-taught, by the way, and know for his cool inventions and ideas, not for his deep mathematical insights).
He also use Pi in computers, e.g to draw circles, and computers (and displays) are even more discrete that nature.
Has he come up with something better to use in Pi's place?
That we don't use "all" of Pi to draw a circle doesn't matter, the "Pi" kind of circle is like the perfect archetype. We don't make the "perfect bridge" or the "perfect car" either, that doesn't mean the concept of bridges and cars is useless.
Yes, it's "only" philosophy, but that doesn't mean it's utter BS.
Look we either talk about the exact pi, or not pi at all. In my computer there's no pi.
As for the alternative, at least he tried something:
"Fuller also claimed that the natural analytic geometry of the universe was based on arrays of tetrahedra. He developed this in several ways, from the close-packing of spheres and the number of compressive or tensile members required to stabilize an object in space. One confirming result was that the strongest possible homogeneous truss is cyclically tetrahedral."
I wouldn't dare to say that about Dr Fuller...
"Mathematics is a way of describing nature, not the other way around."
He doesn't say otherwise, he says that our description of nature (that we are using pi) is flawed.