There's nothing magic about GET, it found old wikis that would allow you to make edits using GET requests. GET being read-only is only by convention, there's no guarantee of what happens server side with GET or any other HTTP verb. It's up to the server.

Possibly via compromised php sites with webshells on AWS and DigitalOcean they could run shell commands to install and use Tor. We don't have forensics of the AWS/DigitalOcean sites although maybe can find signs using shodan etc.