A use statement (as in use module;) evals the contents of a file. The last expression in the file must evaluate to true, or the eval dies.

Not quite. eval never dies based on the value returned by the evaluated expression.

>perl -e"eval { 0 }"

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require (and thus use) dies if the values returned by the module is false.

>copy nul Module.pm
        1 file(s) copied.

>perl -e"use Module;"
Module.pm did not return a true value at -e line 1.
BEGIN failed--compilation aborted at -e line 1.

>echo 1; > Module.pm

>perl -e"use Module;"

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