Like I said, unlikely story

#!/usr/bin/perl --
use strict; use warnings;
use LWP;
use WWW::Mechanize;
for my $class ( qw/ LWP::UserAgent WWW::Mechanize /){
    my $ua  = $class->new;
    warn "$ua\n";
    $ua->show_progress( 1 );
    $ua->proxy( [ qw{ http https } ] => q{http://127.6.6.6} );
    $ua->get( q{http://example.com} );
}
__END__
LWP::UserAgent=HASH(0x99b58c)
** GET http://example.com ==> 500 Can't connect to 127.6.6.6:80 (No co
+nnection could be made because the target machine actively refused it
+.) (1s)
WWW::Mechanize=HASH(0xeb8714)
** GET http://example.com ==> 500 Can't connect to 127.6.6.6:80 (No co
+nnection could be made because the target machine actively refused it
+.) (1s)
Error GETing http://example.com: Can't connect to 127.6.6.6:80 (No con
+nection could be made because the target machine actively refused it.
+) at lwp-mech-proxy.pl line 14.
[download]

Thats both LWP and Mechanize accepting the proxy setting and trying to connect