The answer is "sort of" and "it depends".
If you are talking about the 2.4 GHz band - and this would seem to fit your description best - then he is pretty much talking garbage. The best band to be on is the one with the least noise - both on the main frequency and surrounding frequencies. In this case, Channel 1 sounds better and the tech sounds like he does not know what he is talking about.
If you are talking about the 5 GHz band, its a different story. Different channels in the 5 GHz band have different channel widths and different maximum transmission power - thus in the case it may very well be true that (some) higher frequencies do actually have more power. That said, the channel numbers don't match up very well with what you have posted (Channel 1 does not exist, 7 and 11 are generally not legally useable and are low bandwidth anyway)