I tried 
http://windows.php.net/downloads/snaps/php-5.2-nts-win32-VC6-x86-
latest.zip - I get the same behaviour

host_info and such is only there when you actually have connected 
somewhere. How about you refine your report and try with an actual 
object first?

1. You forgot about the "protected class" mysqli_warning.

2. Then run the following program, and explain its results. I added 
mysqli_stmt only for reference, so that you see the similarity:

<?
function PrintParams($classname, $methodname){
   $class = new ReflectionClass($classname);
   $method= $class->getMethod($methodname);
    echo "$classname::$methodname():\n";
   $parameters = $method->getParameters();
  foreach ($parameter as $param)
  {
    echo "$param : ".$param->getName()." \n";

  }
}

PrintParams('MySqli_stmt','bind_param');
PrintParams('SoapClient','__call');
PrintParams('SoapClient','__soapCall');

?>

3. furthermore - new reflection issues, not really related to MySqli: 
a bunch of interfaces have no extension associated. For example try 
php.exe --rc RecursiveIterator -you'll see that it prints 
<internal:SPL> (which is probably correct). But php.exe --rc Iterator, 
or php.exe --rc ArrayAccess will print only <internal>. 
Coincidentally, this means that you can't find the "Iterator" 
interface in any extension (e.g. using 
ReflectionExtesions::GetClasses) - IMO, it should be either in "SPL" 
or in "standard", but not completely "missing".

Just to clarify - the previous program shows the following results on 
my machine:
====================================================
MySqli_stmt::bind_param():
Parameter #0 [ <required> $param0 ] :
SoapClient::__call():
Parameter #0 [ <required> $param0 ] :
Parameter #1 [ <required> $param1 ] :
SoapClient::__soapCall():
Parameter #0 [ <required> $function_name ] : function_name
Parameter #1 [ <required> $arguments ] : arguments
Parameter #2 [ <optional> $options ] : options
Parameter #3 [ <optional> $input_headers ] : input_headers
Parameter #4 [ <optional> &$output_headers ] : output_headers
===============================================

Notice that bind_param, as well as SoapClient::__call do not return 
any "name" for the parameters (although printing the parameter 
directly will show a name). In contrast with that - _soapCall will 
correctly show the names

Oh, and about your supposition that I need an actual object... that's 
not true, either. Try this:
=======================
$mysqli = mysqli_init();
if (!$mysqli) {
    die('mysqli_init failed');
}

if (!$mysqli->options(MYSQLI_INIT_COMMAND, 'SET AUTOCOMMIT = 0')) {
    die('Setting MYSQLI_INIT_COMMAND failed');
}

PrintParams('MySqli','options');
======================

With the PrintParams function being the one from my previous example. 
I get the following output:
-----------------------
$ php.exe d.php
MySqli::options():
-----------------------

Surprise-surprise, it does get to PrintParams (meaning that it doesn't 
die, and I did successfully create a MySqli object). But what do you 
know, the "options" function still shows as being one with no 
parameters. So maybe they were optional parameters? Nope, this is what  
I get if I give no parameters:

Warning: mysqli::options() expects exactly 2 parameters, 0 given

As it turns out, it doesn't matter if you created one MySqli object... 
the reflection is still buggy.

I found something interesting.
As it turns out, you may need to "refine" the php.net site... the code 
written there seems to be no good, according to your latest feedback - 
because it works just like my example:
http://www.php.net/~helly/classbrowser/class.php?
class=mysqli_stmt&extension=mysqli

And there are others, too, for instance this one:
http://www.php.net/~helly/classbrowser/class.php?
class=DOMErrorHandler&extension=dom
(probably not a reflection bug either, just an unrefined "class.php" 
page)

working on this, needs arginfo here and there. Will be, however only 5.3+

Fix will appear in 5.3.3

Thanks!