No, you're misunderstanding. If the array search returns "0", then the element is found, and it's key is "0". If it returns boolean FALSE then your search term wasn't found.
What it's saying is that if you have the following array:
$array = array(0=>'Windows', 1=>'Mac', 2=>'Unix', 3=>'Linux');
And we want to see if "Windows" is in our array, it will return the key "0" which is also considered "false". But if it's not found, then it will return the boolean false, not the integer that equates to false.