Attributes like killer instinct, speed, power and toughness (both mental and physical) are certainly huge advantages in a "real fight" (heck, they're beneficial in any type of combative context be it sport or real). But, things like weapons, superior numbers, ambushes and other superior tactics can be equally, if not even more important in determining who comes out ahead.
I'd take a 110 lb woman with a blade (who is highly trained in drawing it and employing it), a hot cup of coffee in her hand, and is highly motivated to kill her opponent over either Tyson or Rampage in a real fight. She could likely get very close to a male opponent without setting off any danger signals (especially if she was attractive), and he would not even know what had happened by the time she had blinded him with her coffee and stabbed him in the neck multiple times with her blade.
Now I know that this is more of a murder situation, but since we're talking about real fighting, we have to realize that real fights generally start several different ways:
1) an escalating encounter- there is some violent or threatening verbal/postural dialogue preceding the physical violence
2) an explosive encounter- there is no verbal/postural dialogue which precedes the physical violence, only a sudden unexpected attack
3) a mutually agreed upon encounter- both participants agree to fight (this is the least common form of real world violence, but it's the one that most sport minded people or "though guys" visualize when talking about real fights)
The explosive variety are the most difficult type to deal with (especially if there's a weapon involved) and are also the least morally and legally acceptable type. But this also makes them the most effective type tactically and is the reason that most smart street fighters heavily rely on the element of surprise and being the first to escalate the level of force if need be. Most real fights are not "fair fights".
It depends on their definition of "fighting dirty" though. If they mean that they'd simply wait for you outside your job and run you over with their car, then they'd likely beat you. If they mean that they'd shoot you with their taser gun ,then alternate shocking you with beating you mercilessly with their baseball bat, then they'd probably beat you. If they meant that the minute you started to win 4 of their friends would jump in with bats and beat you, then they'd probably win.
If on the other hand they mean that they'd square off with you UFC style and just pull your hair or pinch you hard, then yeah your superior skill in kickboxing and BJJ would probably wind up with you winning. Keep in mind though that certain techniques are illegal in sport MMA/grappling competitions for a reason, and it's not that they don't work. Having your eye gouged out or getting kneed full force to the balls is going to take the wind out of your sails (at least).