I am glad you taking an interest in the banking system and learning. I hope that you also learned that the Fed is not part of the government, despite the name Federal Reserve Bank, it is a privately held corporation formed by the major banks back in the early 1900's and has remained privately held since then.
If you want an interesting read about "our" banking system go online and find the Federal Reserve Bank's employee training manual titled "Modern Money Mechanics" and learn for yourself that a bank has no risk when they "loan money".
First there is no money. Secondly, the banks can't loan anything they have on deposit. So what they are doing is acting as if they loan you something and the funds are actually created by your signature on the "loan documents". They use a process called double entry book keeping, and while I won't go into all the specifics of it here, just know that at the end of each day they have to balance their books. They do this by creating the money with your signature and opening an account in your name. On was side of ledger is a debit for the amount of money you got and other side of the ledger is a credit for the same amount. The only problem is that these loans have you paying interest on them and nowhere is the interest money created. That is how the people and government have ended up over $23 trillion in debt, is because that money was never created it was agreed upon that you would pay interest, now you have to find somewhere to get it from.
This whole system is a house of cards waiting for a big wind storm to blow it all down. I hope that the documentary you watched explained that the only lawful money in the United States of America is gold and silver coin. We have no lawful money any longer, we have a "money" substitute known as legal tender, it is not lawful money.
I answered the part of your questions about oaths in the comment to @lilyraabe , I hope that answer will explain, if not let me know and I will try to explain it better.
I will say one thing here though that I didn't cover in that reply and it is about that we accept the oaths they take as legit. We accept it because most people don't know what the requirements are, we rely on the media to broadcast these oaths and swearing in ceremonies on public television so we believe everything is as should be and that is a mistake on our part for not learning and knowing how our government was designed and should work, and trusting others to tell us the truth.