The law also says that a cop can't arrest you for no reason but every lawyer will tell you that only means you get a check after the court battle, not that you won't get arrested.

"They have to let you in" means that they don't let you in and you might be able to get a payout in court.

Nobody at the border has the job of "Force the border agent to let in anyone who is an actual American because they have that right", and nobody holds a gun to the border agent's head if he does not let you in.