A grey area where you don't have any rights, if they don't like anything about you they can just put you on the next return flight.

That's if they let you fly there in the first place. I know someone who was denied access because they had a criminal record from over a decade ago, even though it was a minor offence (no prison sentence). This is a UK citizen, so you can imagine how much more difficult it is for someone from a less favourable country.

This is advice for Brits from the US Embassy: "Can you advise me if my arrest, caution, conviction will prevent me from traveling visa free and registering under ESTA? We cannot advise whether a traveler’s specific situation will have a bearing on their eligibility to travel visa free under the Visa Waiver Program. Our advice is that if you have ever been arrested, cautioned or convicted you apply for a visa."

Cautioned! You don't even need to be convicted or even arrested for an offence.

there is the option for a border agent to inspect documents and persons/property like an entry inspection, but the problem occurs when the crossing is not a designated port of entry. They dont have to throw the book at them like they did but "r'spect muh athoritay !" seems to be the predominant mentality.