You should be looking at operator precedence.

open $fh, '<', $qfn || die "...";
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means

open($fh, '<', ($qfn || die("...")));
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You want

open($fh, '<', $qfn) || die "...";
open($fh, '<', $qfn) or die "...";
open $fh, '<', $qfn or die "...";
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In general, one uses "or" when followed by die, return, next, last or similar, and one uses "||" the rest of the time.