So I had 2 more battles with Falkner:
Cheated Zubat for killing Pidgey and cheated Typhlosion for Pidgeotto.
Typhlosion has 9999HP,1 Atk, 999 Def, 1 SpAtk, 999 SpDef, 999 Spd and it's moves have 100 uses (Flame Wheel and Quick Attack).
Pidgeotto used Sand Attack, Quick Attack hits. Pidgeotto again uses Sand Attack and Typhlosion misses. This repeated 2 more turns. Then Typhlosion had too low accuracy so I switched out. Zubat made Pidgeotto fall asleep and I switched again. Typhlosion hit with Quick Attack - Pidgeotto woke up and used Sand Attack - Typhlosion misses every other turn.
The 2nd battle was pretty much the same.
Reverse test: I used my Typhlosion's Smoke Screen once on Pidgeot and Pidgeotto, they hit most of the time (pretty accurate - in the real games confusion and accuracy seemed useless on AI) and my own moves hit every now and then after some Sand Attacks...
Accuracy is working for me, if somebody is encountering a similar problem I will look at that again, but for now I'd say this is no problem with the game.