Seemingly identical action, from the performer's point of view, is performed in a different environment each time it is repeated. Unless you are the Laplace's Daemon, you can't say for sure you repeat the same action over and over because the environment could change in the meantime in an unimaginable way, and that could influence the outcome.
I just really hate that quote because it is detached from reality.
However, with LaTeX, the output of the first run is often an input to the second run, so you get notably different results if you only compile it once vs. compiling twice. When I last wrote LaTeX about ten years ago, I usually encountered this with page numbers and tables of context, since the page numbers couldn't be determined until the layout was complete. So the first pass would get the bulk of the layout and content in place, and then the second pass would do it all again, but this time with real page numbers. You would never expect to see something like this in a modern compiler, at least not in a way that's visible to the user.
(That said, it's been ten years, and I never compiled anything as long or complex as a PhD thesis, so I could be wrong about why you have to compile twice.)
It was 25 years ago, though, but apparently this part did not change.
This said, I was at least sure that I would get an excellent result and not be like my friend who used MS Word and one day his file was "locked". He could not add a letter to it and had to retype everything.
Compared to that my concern about where a figure would land in the final document was nothing.
By coincidence, this is the basic way to compile latex.