During the mi shebeirach for cholim we insert the reason that we temper our cries. On Shabbat, we say "shabbat hi miliz'ok" (the Shabbat forbids us from crying out) and on Yom Tov, we say "Yom Tov hu miliz'ok."
But on Yom Tov that falls on a Shabbat the text in my machzor reads "Shabbat v'yom tov hu miliz'ok." If either one of those is reason enough, why would the text of the prayer list them both? We don't refrain because there are two of them -- we refrain because it is either one of them.