I'm posting a solution to this for anyone who finds this topic through google:
There are two steps required to make Securimage work with ProcessWire:
1. Add this code to the top of securimage.php
ini_set("session.save_path", $_SERVER['DOCUMENT_ROOT'] . "/site/assets/sessions/");
Of course, the path may change depending on where your session path is. This works for those of us with the default path.
2. Change public $session_name on line 382 from null to "wire".
This will ensure that Securimage will validate properly.