I never said it made sense
I can see it in FireFox and Safari, I'll try IE 6 too.
See for yourself:
First load, SID in links, after that, cookie.
Here's the code:
$_SESSION['foo'] = 'Hello World';
<a href="page.php">Link 1</a>
<a href="page2.php">Link 2</a>
<a href="something_else.php">Link 3</a>
<a href="thing.html">Link 4</a>
Is this a server issue? That's my only guess.