Which PDF? I think it is because the PixAxe can only sink/source so much current and the resistor is to limit that current.
EDIT: I think I found the PDF. WIth the 1Kohm resistor right?
Think about it...you connect 5V to 0V through a wire and a switch both of which have essentially zero resistance...how much current do you think flows when the switch is closed? In theory, an infinite amount of current. In practice? As much current as the battery can provide. WIthout the resistor it makes short circuit and that makes stuff overheat, explode and melt.
Yeah, without the 10K resistor, when the switch is closed you have a short circuit between 5V and 0V. Remember, a battery isn't just a voltage- it provides a current too and the resistor is there to limit that current.