I haven't run the query using phpMyAdmin, but I copied/pasted the query from the edit_quotes.php file into the next exercise (delete_quote.php) and I was able to delete quotes:
//Define the query.
$query = "SELECT quote, source, favorite FROM quotes WHERE quote_id={$_GET['id']}";
if ($r = mysql_query($query, $dbc)) { //Run the query.
$row = mysql_fetch_array($r); //retrieve the information.
So, this would indicate that the query works, right? Why would it work in one instance (delete) and not another (edit)? I checked my DB user's privileges and it appears I have all privileges enabled...