The way I look at intimidate is a lot more like Adelei Niska's speech to Mal in Firefly about reputation. Or maybe in Person of Interest when John tells the thug he will burn a quarter million dollars to convince the thug's boss that the thug stole it. Or even in Wizards First Rule when Zed has the peasants describe all the horrible things a warlock can do and then compliments them on their bravery for confronting him. What I'm getting at is, intimidate isn't just flexing your muscles and growling. Or even just saying "I keel you." Intimidate is making the person believe that you will do horrible things to them, their family, their career, or something that they care about. That is why it is charisma based. Can you eloquently and believably state the threat.
In this instance, I probably would have told the players that "f-off or I kill you" isn't enough for any sort of intimidate.
Maybe I am reading too much, but since intimidate specifically uses friendly and unfriendly, I would also be inclined to go back to diplomacy and look at what sort of things friendly and unfriendly allow. And there is a line that states, some requests automatically fail. This might fall in that area.
I agree with this.
Fortunately, the guys I play with are pretty good about talking things out. If they'd truly said "F*** off and die" I'd respond with, "That's what you say to him?". If they said yes, then I couldn't care less what their intimidate roll is. If they say, "Well, no, what I mean to say is...." then I'd take into consideration what they say.
That being said, I think Intimidate and Diplomacy, at least by RAW, has the potential to be too much of a game changer. My players know how I handle the skills, so it's not a big deal for our group. If we had a new player come in, I'd explain it.