rabbonim declaring true things false

There is a phenomenon taking place lately, that Techdirt has named the Streisand Effect. Basically the effect is: the more you do to draw attention away from something the more attention you actually draw to it.

For certain Chazal was highly aware of this phenomenon which is actually a basic part of human nature. This leads me to ask the following question: Is it possible Chazal used this tool intentionally to highlight specific teachings or stories by claiming that the story or teaching was false in order to get people to pay it more attention--without committing to specifically dealing with the content of the teaching or story?

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