I am now able to replicate the issue at my end:
The first two tests were over IPv6 (using the HE Tunnel Broker) and the second two tests were with IPv6 connectivity disabled.
I'm not sure if the TestMy tests fully implement IPv6 support, however, the website itself has IPv6 connectivity. The second ping below is when I re-enabled IPv6 on my network adapter:
I'm not sure if the Hughes Network provides IPv6 connectivity, but if they now do, this may explain the provider identification issue.