Trying my best, actually, real amusement is you quoting Rivera. Even if he were correct (more about that in a moment), his opinion is binding on no one since it is not an appellate decision. (Do I need to explain this?)
It’s true that The People’s Court is not itself authorized to administer oaths. One wonders, however, if they do not take the precaution of having a notary public administer them just as is done in every single other arbitration. Accordingly, Rivera’s decision says nothing applicable here.
Your suggestion that if nothing could be done against Ms. Milian “if she lied” means that she is a liar, is outrageous. For your information, every single sitting judge in the United States enjoys judicial immunity which extends to things a lot worse than lying.
Shame on you.