In my opinion this problem is insolvable, by the information given. This is why:
In order to find the answer you need to turn the question round a bit:
How likable is it that a different coloured ball is pulled and both (A + B) tell A lie about it?
That's 5/6 * 1/3 * 1/5 = 5.55%
So the probability of the statement being true would be the opposite, which is 94.45%
However, that's assuming that they're making their decision completely independent from each other (saying they don't know each other, not in the same room, etc...) which doesn't seem to be the case, as we're told that they AGREE on it being red - you would have to do some hundred years of research on how people from diffrent cultures and ages act in situations like, just to find a statistical probability that's still gonna be a statistic, which is worth ****.
The probability of them choosing the same color for their lie depends, like someone mentioned already, on what lies they're "allowed" to tell. Since we're not told about that, we have to assume they can say whatever they want. Which brings the possability of them choosing the same lie pretty much down to zero, and therefor rises the probability of the statement being true up to....something like 99.9999999% (let's say one of them is a painter and and show of....).
So yeah.... not enough information I'd say. I always hated probability questions which involve human minds, just doesn't make sense to me. But hey, if you can prove me wrong I'm ready to learn...