Wrong, if there is no pull-up resistor and you wire a switch from the input to ground and press the button the input pin will read that as a valid LOW input, no damage will occur. However without the pull-up resistor there is a problem when you release the switch as then there is no valid voltage value wired to the input pin and it is said to be a 'floating input' and will read just noise and can read as either a high or low, so invalid. The only way you can damage a digital input pin is if you apply voltage greater then +5vdc or any negative voltage.
I don't understand, why floating input ? If there is a 5v applied onput should read HIGH. Am I wrong? Also I'm interested what should be the applied voltage for input pin to read LOW?
"applied onput" what does that mean?
If there is a pull-up resistor wired to an input pin (either an external pull-up or the software enable internal pull-up for the input pin) then there will be +5vdc applied to the input pin and the pin will read as a HIGH, conversely if you wire a pull-down resistor to an input pin it will read as a LOW inlput. However if there is no pull-up or pull-down resistor used then the input pin is said to be 'floating' and will not read a reliable value as there is no valid voltage wired to the input pin.