If you're correct...

package Something;
.... #package stuff

sub print {
  my $self = shift;
  my $FH = $self->{FILE}; #deref the FILE handle
  return print $FH join('',@_);
}

#and likewise with others.
[download]

The above would be easier to read and maintain than the whole print { $self->{FILE} } "text" notation, IMO.