In a circuit with a switch and a pull-down resistor, why does the high impedance of the input not discourage current from flowing into pin? I'm a beginner to Arduino and circuits. I've spent the last couple hours hung up on the concept of how current flows through switches and pull-down resistors, having read every thread and watched every YouTube video I could find on the subject. 

I understand that pull-down (and pull-up) resistors are necessary in order to prevent pins from floating. What confuses me is that, if the input pins effectively have a built-in 100 megohm resistance (according to this page), then how is it that a 10k ohm pull-down resistor is enough to dissuade current from flowing directly into ground even when the switch is closed?

Here is a diagram of my circuit:



Am I conflating the high-impedance state of input pins with resistance more generally?

Would really appreciate any clarification on this. Thanks!
Yes, all of the current that flows goes through that resistor to ground.  That way almost all the voltage drops across that one resistor and you are able to read the voltage with the pin on the high side of it.  Only a very very small amount of current flows into the pin when you read a voltage.  It just needs to charge up a very small capacitor.