י and ה by themselves do form a Divine name, used in several places in the Bible (e.g., Ex. 17:16). All of the laws about not erasing a name of G-d apply to it as well (Shulchan Aruch, Yoreh De'ah 276:10).
As for י and ו, we do find those used as a representation of G-d's name in personal names like יוחנן (Yochanan/Johanan, "G-d is kind") and יוכבד (Yocheved/Jochebed, "G-d's honor"). True that there is no law (that I know of) against erasing this combination, but I guess people still considered it too close for comfort.
The point, in any case, is not so much that the numbers 15 and 16 might be used irreverently (they're numbers like any other), but that a piece of paper bearing these numbers, written as Divine names or something similar to them, might be thrown into the garbage or otherwise treated disrespectfully.