provided wrong email address

In PHP, not all methods are created equal.

Normal classes have a structure wherein the declared methods are stored -- the class entry function table. method_exists returns true if a method exists in such table.

But there's another way to obtain methods -- through the get_method handler. See http://wiki.php.net/internals/engine/objects#get_method
method_exists(), if given an instance, calls this handler.

The handler table is associated to instances only; from the class entry, you cannot know which handler table would be used in instances of that class. 

Therefore, it's possible to have method_exists() return true if given an instance and false if given the class of that instance as a string.

In this case, there's a twist. method_exists() also returns false if the  function given by the get_method handler has the flag ZEND_ACC_CALL_VIA_HANDLER, which means the method was generated on-the-fly. This is the case with Closure's __invoke, but the implementation of method_exists has a special exception for the Closure class, and returns true there.

This could be "fixed" by removing the exception and returning false all the time, but this wouldn't fix the bigger issue -- that you can have method_exists returns true with an object and false with the class of the object. So I'd mark this Wont Fix, but let's see if someone thinks otherwise.

Thank you for the clear explanation. 

For anyone interested I found that Reflection gives me the "correct" behavior.

<?php
$lambda = function() {};

$r = new ReflectionObject( $lambda );
var_dump( $r->hasMethod( '__invoke' ) );
$r = new ReflectionClass( get_class( $lambda ) );
var_dump( $r->hasMethod( '__invoke' ) );
?>

outputs

bool(false)
bool(false)