It's by design.
You're supposed to pass a string there, see below:

<?php

function generic_data_handler($specializedFn,$specializedFnData) {
    return $specializedFnData->$specializedFn($specializedFnData);
}
 
class z {
   var $x = 10;
   var $y = 4;

   function _mult($me) {
       return($me->x * $me->y);
   }
    
   function aStupidlyContrivedExample() {
       return generic_data_handler('_mult', $this);
   }
}
 
$a = new z;
print $a->_mult($a);

// an error from the runtime system
print $a->aStupidlyContrivedExample();

?>

So the methodology for this is (what I presume to be)introspection, if possible, I'd suggest the addition to the documentation address the following similar case as well:

class z {
   function b($x,$y) {
       return $x*$y;
   }
}

$a = new z;
$b = $a->b;
$b(3,4) --> an error from the runtime system.

No, you're not requesting introspection here (btw. we will have that in php5). What you want are function pointers. and your second example is only the problem rewritten. Look at sniper's mail for the solution. If you want to pass object and method the notation is array($obj,$methodname).