I mean that you need to run some client software, but it doesn't have to be the client software we're writing. Other people can implement ACME, for example in hosting provider infrastructure or in server software or other configurations. There could be an ACME client where the verification steps indicated to the user are performed manually rather than automatically. You could probably even speak ACME with curl, although quickly generating valid JSON objects that contain valid cryptographic signatures might be a bit challenging. :-)

It's also right that you can have multiple servers and only run the client on one of them, if you're willing to copy key material from one server to another.