If it is really true the FBI will not conduct an interview on tape then there is a rule that needs to be changed. So why don't these lawyers throw it up on the White House Petition page and see if it sticks?
Probably because they understand the cruel joke that the WH petition bonanza really is? And because it is an easy way for smart lawyers to shake of agents for a while, forcing them to look for easier victims that they can threaten.
Thought everyone already knew about the right to remain silent...
You have the right to remain silent if you are arrested. You aren't under arrest; the FBI just wants to "interview" you. However, the law against lying to a federal agent is always in effect. Even if you don't say anything incriminating, if you say something that they can claim is a lie, then they have leverage over you. I imagine that the FBI would also be exceptionally reluctant to conduct an "interview" if you had someone else with you who was also taking notes. Their preferred situation is when there are two of them who can corroborate each others version of the discussion, and only one of you.