I guess that's some inexactness in the documentation of Tie::File. Looking at the source code, there is the following code, which sets/forces $/ to \r\n:

sub _default_recsep {
  my $recsep = $/;
  if ($^O eq 'MSWin32') {       # Dos too?
    # Windows users expect files to be terminated with \r\n
    # But $/ is set to \n instead
    # Note that this also transforms \n\n into \r\n\r\n.
    # That is a feature.
    $recsep =~ s/\n/\r\n/g;
  }
  $recsep;
}
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So, you'll have to read the first few bytes (or up to the first \n), guess the line ending from that, and then use the recsep option to force the line ending.