I think it's possible to hit a human full size target up to 150-200 meters with a H&K MP5 using NATO 124gr ball ammo. I've seen it done with a Steyr Aug A1 Para 9mm SMG and an early FN made UZI 9mm SMG with a wooden stock.
So why wouldn't a Law Enforcement Officer, after enough practice and with suitable ammo, shouldn't be able to do it? They just don't get the chance do it. Most European Law Enforcement agencies train their Officers up to 25 meters with a pistol and up to 50 meters with a SMG. And most of them get limited range time, sometimes just 4 times a year with only 50 rounds.