Doing this identified the object in @headlines as Syndication::NewsML::HeadLine=HASH(0x25055e8). In other words it was already a headline, so of course $h->getHeadLine wouldn't work. I needed to $h->getText and everything worked fine. So the working code segment is:

if (my $newslines = $newscomp->getNewsLines) {
    my @headlines = $newslines->getHeadLineList();
    foreach my $h (@headlines) {
          print "$h\n";
          print $h->getText(),"\n";
    }
}
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