The meaning of this idiom is confusing, to say the least. In a book of idioms, I found another explanation.
It means something that is completely free of dust or dirt.
Here is one explanation that tells about a possible origin of the saying. In the 1700s, a Scottish poet used a similar phrase, "as toom's a whissle." In those days toom meant empty. The idea is you can get the cleanest, purist sound from a whistle or any wind instrument if you keep the reed clean. The reed is the part that makes the sound whenever you blow into it. The reed has to be free of dust or dirt. Here are some examples - The inside of the car is as clean as a whistle. The janitor worked hard and by 4:00, the classroom was as clean as a whistle.