Ah-Ha! That's it!

So, it's not a bug in the code, it's a poorly written doc with an incomplete example.

For anyone else who stumbles on this, this works:

<?php
class Page extends SiteTree {

	private static $db = array(
	);

	private static $has_one = array(
        'MyImg' => 'Image'
	);

	public function getCMSFields() {
        $fields = parent::getCMSFields();
        $fields->addFieldToTab('Root.Main', new UploadField('MyImg'), 'Content');
        return $fields;
    }

}
class Page_Controller extends ContentController {

	private static $allowed_actions = array (
	);

	public function init() {
        $MyVar = $this->MyImg()->getURL();
		parent::init();
Requirements::customCSS(<<<CSS
    .test {
        background-image: url($MyVar);
    }
CSS
);
	}

}

Thanks, everyone for your help! Much, much appreciated.

Chris