I think the no stroking the body is a general rule, as probably most (or at least commonly) parrots will see this as you instigating sexual relations, and lead to frustration and unwanted behaviors. I'm very fortunate that the one parrot who lets me cuddle him, didn't read that memo. I can literally touch, pet, cuddle, restrain with both hands, touch and kiss under his wings or anywhere on his body, etc. Without ANY behavioral problems. He really enjoys it too, and we can cuddle for a long time. Even more astounding is that he's a Red Bellied Parrot (Poicephalus) who thinks he's a cuddly Cockatoo! He's 22 now, and isn't nearly as inclined to bite as he was when he was younger, so maybe his hormones have mellowed out.