Wi-Fi is a shared medium, and all known protocols try to follow this. Whether a router is in a mesh or AP wireless setup, the best performance of the total (overall) system is when all the AP's are on the same channel. That makes it easiest for the routers to share airtime.
If your neighbor's router is sensing/detecting even worse interference from other channels from his adjacent neighbors, it will always pick yours (rightly or wrongly), because you're so close together.
Sometimes, the worse thing to do (counter-intuitively) is to pick a channel from a just perceptible signal from another router thinking yours will overpower it. What happens there is that the two routers must communicate with each other first, before transmitting what is requested, but because they are at the fringe range, they are taking much more airtime to do so.
Are you using 160Mhz width channels, btw?
Nobody asked for you to borrow your neighbor's computer to sign into his router. Just ask him to set a fixed channel. And then see if you pick a different fixed channel is a better result for you.