You can't place variables inside single quotes. Make sure you use double quotes in the global_start hook or you escape out of the quotes.
PHP Code:
// Outputs: Variables do not $expand $either
echo 'Variables do not $expand $either';
$expand = 'YES';
$either = 'NO';
// Outputs: Variables do not YES NO
echo "Variables do not $expand $either";
// Outputs: Variables do not YES $either
echo 'Variables do not '. $expand .' $either';
Check the source code of the page and find the section around the checkbox it should indicate what is going if anything.
Also make sure you surround array keys by single quotes when you write in PHP
e.g.
PHP Code:
// Your version: $template_hook[usercp_options_privacy]
// The way it should be:
$template_hook['usercp_options_privacy']
// N.B. The single quotes