It does matter if antenna is located higher up. This will allow it to pickup weaker signal from clients. Better antenna is also probably more sensitive.
I think what the author meant to express is that the situation is symmetrical, even if one of the antennas is "better" (eg larger, or located higher up). So, author probably meant: "The bidirectional connection is symmetrical. It doesn’t matter (in terms of symmetry) if the AP has a better antenna or is located higher up".
So, even if the antenna on one side is "better" in some way, it affects both directions the same, and as such it still makes sense to use the same transmit power from both ends.
You can also have better analog RF components with more space (filters, LNAs, PAs, etc).
It's not necessarily true that the "advantage" of the AP is symmetric as well. The tx power is limited by FCC part 15 so the difference in tx power between AP and client is probably less than the difference in Rx sensitivity between the AP and client.
Even if the uplink and dowlink are symmetric, the traffic profiles are probably not - there's probably a lot more data going to the client.
1) Hear them better
2) Yell at them louder
(While holding all else equal like transmit power, line loss in the coax...)
With wifi, there is usually little you can do since you probably want a spherical radiation pattern, which prevents you from getting any significant gain over a perfect isotropic radiator, but that's a different story.