What is the authenticity of the story that Parikshit M stayed in a tower to protect himself?

What is authenticity of story like Parikshit maharaj built a one pillared tower where he took shelter of, to get away from takshak’s bite..a brahmana brings a fruit and in it takshak stays…etc etc.,

This story questions surrendered nature of Parikshit maharaj. I came across this story in my child hood Sanskrit text books…probably chapter name “sarpa yag”.

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