That seems like an odd statement. I have had Tennessee Walkers that naturally gaited and could not trot or pace if their life depended on it... Of course we don't ask for the gait 100% of the time, but if that's all they give, then it's what the horse is most comfortable doing. IMO, there's no reason to have a gaited horse trot if its not their natural thing.
I didn't say anything about trotting. The ordinary walk counts as not gaiting too.