True. It happened more than once. Here I have in mind the event at Nazareth at the beginning of His ministry (Luke 4:16-30). Jesus read a portion of Isaiah 61 in the synagogue and claimed that He fulfilled that scripture. His teaching outraged those present. They took Jesus to the brow of the hill on which their city was built, intending to throw him down the cliff. Jesus passed through the crowd and left Nazareth to go down to Capernaum, a town that would become the headquarters for His earthly ministry.
Nazareth is located in the hills of Lower Galilee, where the elevation is about 2000 feet above sea level. These hills lie on the north side of the Valley of Jezreel (Esdraelon, or Megiddo). The hill of precipitation overlooks the Jezreel valley.
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Because it is the precipice (a high point) from which they intended to cast Jesus down. This could be a deadly fall.
Why is it called the Mount of Precipitation?