That's the normal sump capacity, but the transmission actually holds closer to 8 quarts, mainly in the torque converter. Thus the recommendation for the flush. Some say a flush can do harm, but I have no experience with or opinion on that. If your fluid has at least a hint of red in it and doesn't smell bad, it's probably okay.
I would probably try a hydraulic additive, since it's unlikely you'll do any more harm (other than to your wallet). I don't think those products will harm the radiator, but that's something I'd look at more before I used them. I used an additive on a noisy, slipping AWD transfer case once, as directed by a transmission shop, and it worked.