In the case where there is an out as the result of an appeal, if there is any doubt, it should go to the batsman.
It really should, however like DRS, the benefit of the doubt goes the way of the original umpires decision, which was a fair ball. You're right though, the modern day umpire does not pay attention too and call no-balls, which is worrying. I saw some old footage recently and the umpire would turn his head downwards and clearly look for a no-ball, modern umpires maybe glance down if they can be bothered.
In other news, good to see the Pakistanis back at their match-fixing best; all out for 178 on a lifeless road to gift you Englishmen a real sniff at victory in what should have been a draw. Good thing I put a sneaky tenner on you fellas 48 hours ago