Well, if this neighbour is complaining, then they're not the sort you'd invite around for tea. So, if they've not been 'round, how does this neighbour know it's your WiFi and not someone else's that's giving him these headaches?
He probably has his own WiFi setup, sitting there with his anorak and silver foil hat on and his PC running NetStumbler shaking his fist whenever he sees a new network pop up.
Seriously, he, like loads of other Sun readers have seen that and found an excellent scape goat for their headaches. That way, they can pretend it's not their stress, hypertension, bad diet, excessive telly watching and poor sleeping patterns that are making their head sore, it's evil WiFi signals! Then it's suddenly someone else's fault instead of their own. Certainly smells like a Sun article to me.