Did he give any reasoning for that belief? Eg, does assuming non-infinitesimal worldlines improve the predictions of the interference of double-slit style experiments?
Certainly not the latter.
If there were any perceptible grain to them, we'd be about a picosecond from the abrupt end of the universe-as-we-know-it.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.