Hey!
I would like to think I would know something about cat mentality, currently having 7 of the demanding little things at the minute!
But they always seem to surprise me!
One of my girls, Spinks has a very nasty flea allergy, and nothing seems to work during the summer months, and she always has a bald bum! She has steriod injections, piriton tablets (which are impossible to fgive to her these days!) and extra regular flea treatments. However she still reacts all through the summer and it only calms down in the colder muonths, like now when she is growing the coat back on her back end!
Leo however is very much an outdoor cat, and appears every few days for some food, and to sleep all day on the stairs and then off he goes again!
At the end of the day, my job is to feed and love and cuddle my cats when they want to, but could never stop them going out or stop licking their fur til its sore (even when they are pumped full of antihystamines!) so I just let them get on with it!
I'd suggest maybe speaking to your neighbour to let them know you are concerned, as maybe if the cat is out all the time they don't know there is that much of a problem?