Why does modifying my functions.php file always result in a server error

Yup, @s_ha_dum hit the nail on the head. The theme calls the function in a few places. Removing all of those function calls should fix any fatal errors you’re having.

On line 28 of index.php you’ll see how the Twentytwelve theme goes about utilizing the function. Search other files like category.php, author.php, archives.php, search.php and tag.php to make sure you’ll catch all of them.