8 USC 1357(a) Powers without warrant:
Any officer or employee of the Service authorized under regulations prescribed by the Attorney General shall have power without warrant-
(1) to interrogate any alien or person believed to be an alien as to his right to be or to remain in the United States;
(2) to arrest any alien who in his presence or view is entering or attempting to enter the United States in violation of any law or regulation made in pursuance of law regulating the admission, exclusion, expulsion, or removal of aliens, or to arrest any alien in the United States, if he has reason to believe that the alien so arrested is in the United States in violation of any such law or regulation and is likely to escape before a warrant can be obtained for his arrest, but the alien arrested shall be taken without unnecessary delay for examination before an officer of the Service having authority to examine aliens as to their right to enter or remain in the United States;
So he's correct. Even if you don't like it.
He's presumably in the middle of an enforcement operation. He's not obligated to stop doing his job and show his badge and creds to every noodle-brained dipshit demanding to see it. I say "presumably" because I have no idea what video you're talking about, as the only video posted here is in the OP and the only thing I hear is one of the aforementioned noodle-brained dipshits repeating, ad nauseum, "**** you guys."
They can apply, but that doesn't mean they aren't going to be taken into custody that day.