There's no such thing. You're always going to have to be nice to someone - even if you're Mel Gibson.
It also doesn't have to be your employer: it can be anyone you're financially tied to in some way.
I can't give a comprehensive survey of everyone who's made FU money, but take Tim Ferris for example. He's not a whiz at building websites: he just knew to cash in on selling brain supplements online when that stuff was taking off.
Edit: I should point out that I don't think FU money is exclusively about being able to say "FU" to a jerk. I emphasized that aspect just to invert the comment I was responding to. FU money can also just be about ditching a career you're not that interested in (but may be highly skilled at, and otherwise locked into).
To me, I don't have FYM, despite meeting your threshold 8x over. It would not be easy for me to replace my current income at another job. (I'm 7+ years here, know our tech and business inside and out, and am paid pretty fairly for that, but that doesn't mean that I have nearly the same value to another company, something that headhunters who call have a hard time grasping when I tell them my comp range.)
In fact, the people that have 'fuck you' money (that I know) tend to be pretty rude to people that are simply trying to make their lives a little easier, such as people waiting tables or running a store. You can instantly tell from the way they treat those 'below' them in stature (if there is such a thing anyway, my grandmother used to say about such people that they smell just the same on the toilet) whether they're nice or not.
As a rule, if people are rude to others that are in a 'lesser' position to them then you can do without them just fine.
It hasn't affected me much, I still work, I'm still kind to strangers and waitresses. You're rule is good, but something tells me those people you know would be the same in any situation.
That's exactly why the rule is good, it allows you to pick out people like that. In other situations they will be the same (they can't help it) but it won't stand out so much.
Some people try to impress others by bossing people around or showing they can afford to be rude, for me that's a total turn-off.
The really interesting thing here is that the really wealthy are usually quite modest (at least, those that I've met, which is not a very large sample).
The people I know with FU money have generally been really nice - there was this one kid in college who was an asshole, but he's the exception, not the rule. Most will go out of their way to help people, and are always polite to waitstaff etc.
Maybe I've just been lucky. I've found that the comment someone made in the original thread holds pretty true. ("Whatever type of person you were before FU money, you'll be more of afterwards. If you were a jerk beforehand, you'll be more of a jerk afterwards, while if you were a nice person beforehand, you'll be a nice person afterwards.)