Grant may have gotten drunk a time or two but his bosses/Generals over him were far greater liars and back stabbers then Grant ever was a drunk. Most of the rumors about grant being a drunk were lies. Eventually those back stabbing political Generals over Grant were fired or knock down the ladder a few rings.
Ironically, those former generals-in-charge who remained in the army did a good job in subordinate positions under Grant and Sherman. Joe Hooker, for example.