I'm not a Fed or a lawyer; nor do I play either on TV. I read a LOT of Federal Regulations as part of my political science program, so here's my best shot at it, plus the various conversations, ground instruction, and so forth that I've had.
How far does this chain of culpability go?
I would presume it starts after passengers are onboard and ends after they are off the airplane. From boarding to deplaning - while the aircraft is being operated.
A selection of pertinent Federal Regulations:
14 CFR 91.3 states that the pilot-in-command is directly responsible for, and is the final authority as to, the operation of an aircraft. Command means just that: you are it, from the student on a solo to the Captain of an Airbus 380-800. The legal authority and responsibility are the same.
(The regulations really illustrate that some smart lawyers work(ed) at the FAA. The above regulation is sufficiently vague such that, in most circumstances, if you have to exercise your authority you are legal to do so. It also means that the FAA can call you on the carpet to 'splain yourself. The vague nature of the regulation is there to give both you and the Feds considerable latitude.)
Carriage of marijuana, depressant, stimulant, or other narcotic drugs, aboard an aircraft, is prohibited (91.19).
Carriage of "a person who appears to be intoxicated or who demonstrates by manner or physical indications that the individual is under the influence" is prohibited. (91.13) The way I understand it, the pilot-in-command shall refuse to carry such individuals. It doesn't matter who owns or pays for the aircraft.
Passengers getting intoxicated on board the aircraft is not specifically mentioned in Part 91, although I would imagine 91.11 - Prohibition on interference with crewmembers might come into play, and the above part about not carrying drunk people applies. Part 121 and 135 air carriers must stop serving passengers who appear to be intoxicated or otherwise demonstrate that they are intoxicated.