Right, though I don't think uniform is the necessary condition here. We only need a positive chance of picking an R so that f(A) and f(B) are on different sides of R, which isn't as much of a problem if we're picking R from (-1, 1).
There's also the question of how the first two numbers were chosen; in other words, what it means that 'the numbers are completely arbitrary'.
I can't math real good, but this is the part that smells fishy to me.
So long as you have a non-zero chance of your number "R" being between A and B, you have an advantage.