The documentation leaves out the important case of new properties you add to objects at run time. In fact, property_exists will return true if you ask it about such properties.
<?
class Y {}
$y = new Y;
echo isset( $y->prop ) ? "yes\n" : "no\n"; // no;
echo property_exists( 'Y', 'prop' ) ? "yes\n" : "no\n"; // no
echo property_exists( $y, 'prop' ) ? "yes\n" : "no\n"; // no
$y->prop = null;
echo isset( $y->prop ) ? "yes\n" : "no\n"; // no;
echo property_exists( 'Y', 'prop' ) ? "yes\n" : "no\n"; // no
echo property_exists( $y, 'prop' ) ? "yes\n" : "no\n"; // yes
?>