Not only

On localhost, /test01.php is in session table; not on ISP...
So...
I've asked my ISP to migrate one of my accounts to PHP 5.1.5 & MySQL 5.0.22 and then I have installed a copy of vB on it (yes, I know it's illegal, but I will delete it, don't worry) .
Same test page but this time : good results on WOL page and $filename contains the correct file name.
Apache server is still the same.
So it appears that my problem is related to the version of PHP running on the server.