Good question!
Increasing the tx-power does cause more co-channel-interference (CCI) to other APs and clients. However there is more interference than CCI from your own network, like other WiFi signals and non-WiFi interference.
Just looking from the AP and associated client, the higher the tx-power, the higher the signal-to-noise ratio (SNR), the higher modulation and data rates can be used. This improves the radio link robustness and performance.
As you can see, there are conflicting rules here. You want to have the tx-power as high as possible for the best links and the highest data rates, but on the other hand, you want them just high enough to not cause too much CCI to other APs and devices in the complete system. This is why you need to get to a balance of these two, where the total system throughput is leading while still optimizing wherever possible the individual AP and client performance.
What is pretty cool about AirMatch is that it calculates that optimal point, and by changing, measuring, optimizing it will get to the best overall system performance.
So you were right from a total system performance perspective (in a perfect world without interference), the Techbrief is correct from the AP-client perspective and other networks/non-wifi interference; and both need to be seen in balance.