This reminds me of a story.
My mom was running a day care out of our house, and she had a a few that had binkies.
One family was trying to break their son (Lenny) of the binkie habit. He was determined he was going to keep it.
One day, he arrived without his binkie, and after Lenny's parents left, my mom said: "Lenny, where is your binkie?"
Lenny got wide-eyed and replied "The mow-mow took it!"
Mom: "Um....what?"
Lenny: "The Mow-Mow lives in the cellar, and he eats binkies, so he took my binkie."
We could not BELIEVE his parents told him that.
I'll have to say that doesn't sound like an entirely bad idea.
Apparently Lenny bought the story. By the time he's old enough to understand anything, he won't remember it. He seems to have accepted it as an adequate explanation of why he can't have the binkie. And if he's old enough to understand supernatural concepts and speak in full sentences, he probably is too old for a binkie anyway.
After all, parents keep up the pretense of Santa Claus until kids figure it out when they're like 8, so this doesn't seem that much different. Except, well, in a scarier way. Now Lenny doesn't just have to worry about a home invasion from one strange man once a year -- now the monster lives in the basement and is there all the time!
Is it possible one of his parents drove over the binkie with a lawnmower? I realize Lenny may have lived in a part of the city where there aren't lawns to mow, so just a thought. If it were a mower, it would fit the story except he'd have confused the cellar and the garage.
Side note: On that other thread, we were discussing American vs. British names for things. I wrote the sentence above before rereading your post and realized I had said "basement" and you had said "cellar." I wonder if that's an East Coast/Midwest linguistic difference. I guess as CellarDweller, you would know!