Answer

The Beit Yosef on the Tur there cites this Gemara straightforwardly. That is, he does not see this as a difficulty. It seems his intention is to say that it is permitted to wrap them in one cloth, but if they did touch then they certainly must be rinsed off. And in the Gemara he apparently understood that there is no prohibition on wrapping them even if they touch; rather, if they did touch there is a prohibition on eating them unless they are rinsed before eating. According to his approach, it seems the Gemara should be read like this: it is permitted to wrap them in one cloth, and there is no obstacle to eating them—for regarding the mere placing of them in one cloth, if one is not eating them, there is nothing to discuss. Why should that be prohibited?! So the prohibition and permission being discussed there relate to eating, not to the wrapping in the cloth. Except that if they touched one another, then they must be rinsed before eating. But it is still permitted to place them there. When he writes that "we are not concerned that they may touch," he does not mean that there is no concern that they will touch. On the contrary, if they are in one cloth it is obvious they will touch. Rather, we are not concerned with this in order to prohibit the very act of placing them in the cloth (wrapping them). It is permitted to place them there, and if they touched, one rinses them before eating.
I later saw that this is apparently what the Perishah there meant as well.