I've heard something like that from a non-physics person ten years ago, later then asked a person who actually studied Physics about it, and he claimed it was bullshit?
Specifically, the Planck Length is described as:
It is the smallest distance about which current, experimentally corroborated, models of physics can make meaningful statements.[2] At such small distances, the conventional laws of macro-physics no longer apply, and even relativistic physics requires special treatment.
Here's the article and citation: https://en.wikipedia.org/wiki/Planck_length#cite_note-3
And a Planck time unit is the time it takes light to travel that distance.
Naturally, this doesn't necessarily imply that time, too, has to be discretely divisable, so I think I can understand how the person who studied physics sees it...
[0]: https://en.wikipedia.org/wiki/Coastline_paradox
EDIT: On the Coastline Paradox, it's stated on the Wikipedia page (I had just thought, and linked, without reading):
> "As the length of a fractal curve always diverges to infinity, if one were to measure a coastline with infinite or near-infinite resolution, the length of the infinitely short kinks in the coastline would add up to infinity.[3] However, this figure relies on the assumption that space can be subdivided into infinitesimal sections. The truth value of this assumption—which underlies Euclidean geometry and serves as a useful model in everyday measurement—is a matter of philosophical speculation, and may or may not reflect the changing realities of "space" and "distance" on the atomic level (approximately the scale of a nanometer). For instance, the Planck length, many orders of magnitude smaller than an atom, is proposed as the smallest measurable unit possible in the universe."
EDIT2: > "smallest measurable unit possible" ...oh no... we still have to go deeper!