The docs you quoted support me. perlvar and some variables outsides of perlvar don't need to be declared. My snippet lists all the variables in perlvar AND the variables not listed in perlvar that it acknowledges. I did mean to mention the non-text variables from perlvar (e.g. $^W) don't need to be declared either.
Note that both of these still leave out $a and $b, which are subject to the package statement yet do not need to be declared via use vars to be used inside a use strict environment.