All joking aside regarding the denial of entry into the US for being drunk. The short answer is that a US citizen is entitled to entry into the US. However, this is not entirely true. There are classes of US Citizens that can be denied entry in the US. What are those groups.

The first group are those that hold dual citizenship. These folks fall into the group that the inspector determines are not really US citizens. This can be caused by being later nationalized into another country that requires you to renounce your citizenship in another country, or one that prohibits the possession of another citizenship when you acquire theirs. This situation is more commonly found countries where one spouce automatically acquires the citizenship of the other spouce upon marriage. The effect of the marriage could be seen by the agent as a renouncement of your US Citizenship. With the amount of information the US desires from airlines this issue is cropping up with more frequency, though it is still very rare. One of the pieces of information that is requested is the passport the passenger used on all legs associated with that ticket. (Example is that on flights back from TLV an dual Israeli/US citizen is logged in the system as having enter Israel on an Israeli passport, but entering the US on a US passport.)

The second group of persons who can be denied are those persons holding US passports and hence citizenship from the former trust territories that have not entered into the compact of free association with the US. I don't know if these are still around, but they work very similar to the British Overseas Passports.

The third group is US citizens who are intoxicated at the time they try to enter the US. Basically the law gives the inspector two choices. 1) Admit the person to the US and arrest them immediately. It is a crime, and I believe it is a misdemeanor to enter the US intoxicated. or 2) turn the intoxicated person back. Most inspectors will do the second one. At the airport, due to other issues, they just send you to the holding pen and let you sober up. Of course to get to this point you have to be very very intoxicated. i.e. you reak of booze. At the land crossings all they do is turn the car/person around and send them back to either Canada or Mexico.

Basically, two of the grounds of rejection come from the Inspector questioning the actual citizenship of the person. Hence the US passport has not "proven" to the inspector that you are a US Citizen. The third is for violation of a law, and the inspector is being nice.