Both Ilia & Derick said it's a docu problem.
Reclassified.

This bug has been fixed in the documentation's XML sources. Since the
online and downloadable versions of the documentation need some time
to get updated, we would like to ask you to be a bit patient.

Thank you for the report, and for helping us make our documentation better.

The filter_var() vs. the filter_input() behave differently when using the 
FILTER_VALIDATE_BOOLEAN filter when the variable/input doesn't exist.

More specifically, it seems as if the FILTER_NULL_ON_FAILURE flag is set 
automatically in the filter_input() function.

(Note: same behavior for filter_var_array() vs. filter_input_array()).

<?php
// example.com/script.php?arg1=yes&arg3=no

// filtering by variable
$var1 = filter_var($_GET["arg1"], FILTER_VALIDATE_BOOLEAN);
$var2 = filter_var($_GET["arg2"], FILTER_VALIDATE_BOOLEAN);
$var3 = filter_var($_GET["arg3"], FILTER_VALIDATE_BOOLEAN);

// filtering by input
$input1 = filter_input(INPUT_GET, "arg1", FILTER_VALIDATE_BOOLEAN);
$input2 = filter_input(INPUT_GET, "arg2", FILTER_VALIDATE_BOOLEAN);
$input3 = filter_input(INPUT_GET, "arg3", FILTER_VALIDATE_BOOLEAN);

// as expected...
var_dump($var1);      // bool(true)
var_dump($var2);      // bool(false)
var_dump($var3);      // bool(false)

// NULL is not an expected return unless the FILTER_NULL_ON_FAILURE flag is 
set...
var_dump($input1);    // bool(true)
var_dump($input2);    // NULL
var_dump($input3);    // bool(false)
?>