Does a backquoted command automatically get output to stdout as well as into the string $result?

No. You can't have the cake, and eat it too.

BTW, stderr is caught as well.

$result=`cat $file | anotherscript.pl`;
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I think this gives you a nomination for the Useless Use Of Cat Award ;-) But from the Perl side, you might consider to assign to @result, not $result, because this spares you from using split afterwards. But don't forget to chomp the lines afterwards. You might also consider something like this:

# Note: Code untested!
my @none=grep { chomp; /NONE$/ } qx(anotherscript.pl <$file);
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And don't forget to use strict and warnings....