As far as I can tell, your analysis is correct.

Did I find a "mistake" in the wonderful Perl Testing book?

I unfortunately don't have the book so I can't check the exact wording, but you did write the following, to which I added some emphasis:

the book says it's necessary to have the script being tested (a cgi script, in my example) end with the statement "1;" so that the require_ok() in the testing script will always work

That sounds to me like maybe what the book means is "to play it safe, always end the script with 1;, in case someone tries to get clever and writes if !caller instead of unless caller" :-)