The trick here (in this Wi-Fi example) is that the end you control is the end with parabolic antenna - if you can make it to collect enough energy for RX from an omnidirectional source, you can also make it send enough energy towards that source for its antenna to pick it up.

But you're right that "every improvement in sending is completely equivalent in receiving for a system that uses the same antennas for both directions of communication" is wrong; there are different ways of improving TX and RX, even though some overlap a bit, to some extent.