To address the issue in the article, I expect that if Chorus / Telecom received a request to tap your connection you will never know that they have tapped it. The dark fibre circuits we have through them are provisioned on day one with an optical tap that is configured to direct a small percentage of the light to any gear that they might one day connect to it. The latency would be completely unaffected.
What makes more sense given the story is that Dotcom was on a fast fibre tail using a service that was actually in Sydney somewhere ( ~30ms away ) and for whatever reason this service switched to a node in the middle of the USA which could be 180ms away. Nothing there to do with taps or government conspiracies. They may well have been tapping his circuit as well, but the latency won't be anything to do with it. Even if they did have to divert his connection through some GCSB site, the latency would not be as high as 180ms.
As far as ping times to perth, from the same box in skytower:
[ ~ ]$ ping www.perthix.com
PING www.perthix.com (22.214.171.124) 56(84) bytes of data.
64 bytes from 126.96.36.199: icmp_seq=1 ttl=120 time=81.3 ms
64 bytes from 188.8.131.52: icmp_seq=2 ttl=120 time=80.1 ms
64 bytes from 184.108.40.206: icmp_seq=3 ttl=120 time=81.2 ms
--- www.perthix.com ping statistics ---
3 packets transmitted, 3 received, 0% packet loss, time 2002ms
rtt min/avg/max/mdev = 80.181/80.933/81.383/0.628 ms