So what do you believe should have happened to the woman who was kept from entering the country? How should it have been handled?
I am thinking that it was probably handled correctly.
The agents are the ones that inspected her documents.
It is not unreasonable to think that her documents were at least "questionable".
The agents held her to question her - again not unreasonable.
In the end she said that she is not a citizen.
Based on that they should not have allowed her to enter the country - especially if she was trying to present herself intially as a citizen.
If the documents were forged then keeping them was the correct thing to do so that she could not use them to attempt to reenter the U.S. at a different crossing at another time.
If you were the border agent and someone presented you with documents that you did not believe what would you have done?
Simply let her enter the country?