Really depends on the applicable law in the jurisdiction. In Washington, we used to call these "interim drinking defense" cases. They usually followed a pattern of an accident, often one car vareity, then the person left the scene and was arrested either upon returning or being located elsewhere (often at home).
Used to be easier to win these, but the legislature shifted the burden on the defense a few years ago to require the defense to establish the defense by a simple preponderance--in other words, assuming the prosecution could otherwise establish the elements of a DUI beyond a reasonable doubt, the defendant could still have a shot at acquittal if he/she could establish that it is more likely true than not that the intoxication actually arose AFTER the time of driving.
These sort of cases are still winnable in Washington, but you need decent facts to make it fly. Years ago, I actually won a DUI using this type of defense where the client's blood alcohol content was .26%. I'm sure I won at least a couple others that way, but that one stands out in my mind.
As far as public intoxication, not every jurisidiction outlaws that. Besides, if the guy was swilling a bunch of alcohol at the time, you can't necessarily assume he was intoxicated at that very moment. However, the list of possible acts that might be outlawed there is virtually limitless. Public consumption, open container, obstruction, etc. The more interesting question, to me, is how the guy was able to get his hands on more booze after being stopped for suspicion of a DUI.
