A 500 can also imply that something failed in LWP::UserAgent:

    if ($use_eval) {
        # we eval, and turn dies into responses below
        eval {
            $response = $protocol->request($request, $proxy,
                                           $arg, $size, $timeout);
        };
        if ($@) {
            $@ =~ s/ at .* line \d+.*//s;  # remove file/line number
            $response = _new_response($request,
                                      &HTTP::Status::RC_INTERNAL_SERVE
+R_ERROR,
                                      $@);
        }
    }

...

sub _new_response {
    my($request, $code, $message) = @_;
    my $response = HTTP::Response->new($code, $message);
    $response->request($request);
    $response->header("Client-Date" => HTTP::Date::time2str(time));
    $response->header("Client-Warning" => "Internal response");
    $response->header("Content-Type" => "text/plain");
    $response->content("$code $message\n");
    return $response;
}
[download]

The "Client-Warning: Internal response" confirms that the problem is on my end, not the remote server end.