The one thing that convinced me of that is the sudden jump in realism in Egyptian art during the reign of Akhenaten (Amarna period, see the famous Nefertiti bust for a great example). The new king asked for more realism and he received it, it just took a reset in conventions.
[0]: https://en.wikipedia.org/wiki/Perspective_(graphical)#Early_...
There are some words in people's explanations that always bother me. These are 'just', 'mere', merely' and the like. Why? Because they're not explaining, but explaining away. It's like saying: x is trivial, so it's not as important as you think.
But reality is much more complicated than that. For even simple things are hard to fathom for those not knowing how simple it is.
Now, back to the topic: no, medieval painters' lack of knowledge on how use perspective was not just matter of being stuck at conventions. When everyone is expecting to see a certain thing and you're payed to do that thing, it's not 'just' up to the painter see outside her/his perspective. What I'm saying is that takes a huge leap to break away from all that.
Beware of just explaining away phenomena.
Back in context, what the parent is saying is that the grandparent provided a "just-so" story: The parent finds it easy to believe that history happened in a way which neatly lines up with the story that they are telling. Did earlier humans know about perspective? Grandparent believes that it's obvious.
The explanation for that is generally agreed on to have more to do with the aesthetics of early Christianity influencing Medieval practices, more than changes to human perception (source: I have a masters degree in Art History).
That said, up until the European middle ages, nearly all art was that which was commissioned by the church. The style of the time permeated the art that wasn't commissioned by the church. As more non-religious art was commissioned, there was little need to remain working in that style and realism was embraced. I could be wrong, and probably am, but I think Catholicism is the only large Christian denomination that adopted realistic art.
I think depth was already understood by this point, though (see sculptures[2]). Again, I'm not OP, and I'm sure OP will have a more thorough explanation.
[0] https://orthodoxartsjournal.org/topics/iconography/
[1] https://www.britannica.com/event/Iconoclastic-Controversy
You can see the intent on many religious sculptures in medieval churches around e.g France: the technique is precise, so it’d be really easy for a sculptor to just compare and match to a living and breathing model, therefore they chose not to. Contemplating how churches tell stories through imagery, you can see how they used this style for emphasis on specific physical features to elicit strong emotional response instead, not entirely unlike those TVs in stores cranking up contrast to completely unrealistic levels.
You wouldn't want to draw mere mortals bigger than saints just because they happen to be closer. Peasants (which couldn't read and were the main target of these paintings) could get wrong ideas.
https://upload.wikimedia.org/wikipedia/commons/f/ff/Francesc...
[1] https://journals.sagepub.com/doi/10.1177/053901847000900411 - Church Time and Merchant Time in the Middle Ages - Jacques Le Goff
Mimicking reality is rarely the goal that art is optimized for. It's mostly converging to local optimum of one of the current fads.
I was an artist for a while. It wasn't that artists couldn't depict depth. Fashion, religious instructon, and to a lesser extent materials, is what decided which paintings and frescoes lasted the test of time.
You can still find people who are just as "unchallenged" as a medieval peasant today. Look in rural places of countries like china.
So I think ancient discoverers wasted a lot of time rediscovering things.