There is no such thing as "fatigue neutral" round after round being attacked multiple times. Even when enemies miss you you lose fatigue. Works on other origins where you can get decent amounts of base fatigue, but with a level 7 cap? It might work early to midgame, but I am skeptical about late game specially against certain types of enemies.
You don't understand how the fat recovery works. When you get your turn, you regain 15 fat. Even if enemies hit you 200 times, and if you're fighting for 10000 turns, your bro will still recover 15 fat when it's his turn, enough to move one tile and swing a 2h weapon once with mastery.
Fat neutral builds exist to take advantage of that. You need only ~20-30 usable fat on them, can be as low as 15 but then sometimes you'll get screwed by injuries that penalize fat. Being able to completely ignore fat frees up a lot of stat/perk points that normally a battleforged bro would need to take + lets you completely don't care about armor fat penalties, just throw the heaviest shit you have on them, as longh as they have 15+ fat left it's cool.
It's a build you normally take when you have bros who don't have enough fat for BF, or HP/INI for good nimble, but have great MA/DEF. Very nice for great swordmaster recruits for example. Or for indebted who lack in most stats and have heavily limited perks. You don't need brawny, you don't need recover, you only need pathfinder (so you can move + attack on most terrains) weapon mastery (can be skipped with -fat cost famed weapon, or if recruit has iron lungs) and battleforged, rest you can pick whatever you want and it will still work.
The whole point of the build, is that your indebted will be able to ALWAYS move one tile and swing 2h weapon, regardless of their fat (except on shit like swamp, but everyone is fucked there anyway)