“a video recording to which you have access, being made of the proceedings.”
Do the FBI and law enforcement agencies allow that?
Generally speaking, the FBI does not. This is because the FBI has a policy that there will not be any other recordings of the meeting. This is a legal tactic used by the FBI to insist that their version of the interview, and ONLY their version, based on the FBI agent’s notes, is entered as evidence. It can be and has been used as the supporting evidence for charges.
However, a smart lawyer will insist that the conversation be recorded - video preferred. If the FBI does not want that, then they don’t get to question you in person. They can then submit the questions in writing to your attorney who will then provide the most appropriate response.