liar liar pants on fire

Robert B.Parkerの "Painted Ladies"を読んでいます。
The other girls hadn't mentioned the painting. It wasn't secret. But you needed to be interested to remenber that the infernal device had been the painting, or something everyone thought was the painting.
"I'm going to be late," Missy said. "I wish you wouldn't bother me about this anymore."
"I'm sure I won't need to," I said.
She scooted off into the science building. I watched her go.　"Liar, liar, pants on fire".

最後に出てきた "Liar, liar, pants on fire" の意味は何でしょう？　Missyが嘘をついていると言っているのはわかりますが。　辞書を見ます。　"pants on fire" で調べると：

・Wiktionary: Clipping of liar liar pants on fire.
そこで "Liar, liar, pants on fire" で見ると、
(childish) used to taunt a liar
・Urban Dictionary: to lie so badly that, theoretically your pants will burst into flames. popularized by the kindergarten chant, "liar liar pants on fire!".
・Wikipedia: "Liar, Liar, Pants on Fire!", a playground song about lying

なるほど、子供が相手の言うことをなじる時に使うのですね。