Do you think you're more likely to encourage an FBI officer to decide you are "agitated" if you insist they come back with a warrant and slam the door on them, or politely and cautiously answer basic, non-incriminatory questions on the assumption you're probably not guilty of whatever they're investigating? You can always pull the "if I'm being implicated in a crime, perhaps we should go down the police station and have a recorded conversation with a lawyer present" tack later if the questions start going uncomfortable places.
Coincidentally, I also received a totally unexpected call from police earlier this week. I wasn't suspected of committing a crime. Apparently helping them get in touch with my flatmate - who unbeknownst to me had reported a crime - didn't incriminate me or my flatmate. Don't get me wrong, I'm sure a lawyer would rather I had that two minute conversation in their paid presence, but I'm not really sure where they'd have helped me avoid accidentally intimating that I might be a criminal: I think I'd have done that more effectively by automatically assuming I was being investigated.
Assuming instantly pleading the Fifth helps misses the bit where police and especially more powerful organizations like the FBI jump to and act on a lot of conclusions that aren't admissible in court (and of course have plenty of capability to find non-verbal, admissible evidence of wrongdoing if motivated to look for it, even if you're innocent). If they're casually following up a dubious lead, which they probably are if you're not expecting their visit and don't have pot plants or a server mirroring Wikileaks in your conservatory, you probably don't want to fit their mental model of a suspect, which probably means you being at least slightly curious about why they want to speak to you, and at least willing to entertain the possibility that you're not the suspect. Statistically, you're more likely to plead the Fifth if you're guilty.
(This probably doesn't apply when they're picking on you because you're a genuine suspect or there are political reasons for them trying to find out about your friends or organization.)
There are indeed times when subdued appeasement and "friendly banter" as negotiation tactic may be a good/best course of action.
FBI knocking on your door wouldn't be one of them though. At least for me, but to each his own.
manish_gill's linked video is an amazing example of the information/power asymmetry working against you in this game. By the time you realize you're in an "uncomfortable place", it's likely too late.
