You have very few rights at a border. Almost any border, not just the US. A border is very much like a no-man's land where the law of the country you are entering or leaving is suspended. You can be held, searched without cause, refused entry at a guard's discretion (no reason is needed), and so on. Arguing your 'rights' at a border is one very good way to be seen as cause to get secondary screening and perhaps refusal of entry. And they are pretty good at detecting if you are lying - lots and lots of training there, you'd be surprised how easily unprepared people give themselves away in even the most simple lies.