A person is allowed to wrap a piece of meat and a piece of cheese together in one cloth, but they are not allowed to touch. They cannot touch whatsoever, even if they are cold, because the spot where they touched may have rubbed off some of the meat onto the cheese, and vice versa. So when somebody eats them, he will be eating both of them together, which is an issur de-Rabbanan (rabbinic prohibition). A person would have to rinse off that part before eating them. We are nervous that a person will forget to rinse it off and end up eating it, violating a rabbinic prohibition by eating this in one shot. So we do not allow them to touch whatsoever.
If two guests are staying together at a hotel, do not know each other, and are sitting at one table, one eating meat and one eating cheese, they are allowed to sit at the same table. We are not concerned that their foods will mix. They do not know each other, and we are not afraid that one of them will take the other’s food and mix it into his own. Therefore, the whole chashash, the whole nervousness of the last Mishnah—that by putting meat and cheese together on a table where people are eating, they will end up falling into each other’s food, being near each other, and taking food from each other—does not apply in this scenario.