I know the answer to this. In 2014, the thing that keeps the police from saying anything else is a recording of the entire situation. Recording is standard practice in most interrogation situations. I say most, not all.

Story Time; I was interviewed for a crime I was tangentially related to (my employer at the time was robbed while I was on the clock, they were investigating any possible connections on my side). I kept repeating, "I would like to speak to my lawyer please." Once my lawyer came, he advised me to just be honest and tell them that there was no connection. I was just uncomfortable about talking to a cop behind closed doors and was 17.

When asked what we talked about, the cops response was something along the lines of, "nothing, the little asshole just kept saying lawyer. Check the tapes."

It was then that I realized the power of video.

The FBI recently changed its long-standing policy of not recording interrogations.

> Let's say they arrest me, put me in a room and try to interrogate me for a few hours before a lawyer shows up. Even if the only words out of my mouth the entire time are "I would like to speak to a lawyer please", what stops the Police from saying I said something else entirely?

Their conscience about committing perjury. Nothing else.

But it's a bit more nuanced than that, because even if each one of the people in the room (aside from you) are willing to commit perjury, each one has to be convinced that each of the others is also willing to commit perjury.

Right. An outright fabrication from pure silence is less likely than a creative "misinterpretation".