In the Programming Perl, 3rd. ed, p. 96, stat is listed as a named unary operator, is that a mistake?

No; rather, a named operator is a function. Or at least, Perl builtin functions are operators; either list operators or named unary operators.

Take a look at the first section of perlfunc.

The Sidhekin
print "Just another Perl ${\(trickster and hacker)},"