How to check False booleans when using get_option?

You can set a default value for when the option does not exist. This way you can check to see if the returned value is false, or if it doesn’t exist at all:

$value = get_option( 'my_option', $default_value );
if( $value == $default_value ) {
    // Option does not exist
} elseif ( $value == false ) {
    // Option's value is equal to false
}