When you build a small house, you don't account for the curvature for earth. Same for when you walk down the street.
When you build a runway for a plane or a long bridge, you do.
A model is not necessarily useful in all contexts. People still use the flat earth model in useful ways because it's simpler to assume the earth is flat in some situations. Of course, once you go beyond the capabilities of the flat earth model your numbers will wildly diverge into the realm of useless while the round or spherical models provide useful numbers for longer.
If parent had been talking about chemistry or physiology or any subject that can be explored via controlled experimentation, I wouldn't have complained. Instead the topics were geological and evolutionary history, which seem very much not "empirical". Not that I suspect that those sciences are wrong in any sense, but words have meanings.
I misread gp as saying "flat Earth", and not "young Earth". My apologies. I would agree that even if we can point to things like nylonase or the speed of light coupled with known distances to stars, those are deduced facts. Whereas astronauts have empirically observed the spherical nature of earth.